European Mathematical Society - Eugenia Cheng
https://euro-math-soc.eu/author/eugenia-cheng
enThe Art of Logic
https://euro-math-soc.eu/review/art-logic
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is a book about applied logic. Books that popularize mathematics (and logic) often have chapters about paradoxes, or logic puzzles. If you were expecting something in that style, then it will soon become clear that you are mistaken. Eugenia Cheng who combined in her previous book <em>Cakes, Custard + Category Theory</em> her profession as a mathematician specialised in category theory and her hobby of cooking. In <em>Beyond Infinity</em> she discussed the infinitely small and the infinitely large, which is also rather mathematical, but it can also lead to paradoxes such as the Hilbert Hotel.</p>
<p>
In the current books she discusses the roots that govern all mathematics: the rules of logic and axioms that lay at the origin. Close as this may be to the heart of a mathematician, she considers here however how logic also applies to our daily life, although in a much fuzzier way and lacking the mathematical formalism. As a consequence misunderstandings will occur. These will result in endless and unsolvable discussions, because the opponents apply different rules or different axioms and so both claim to be correct in coming to opposing conclusions.</p>
<p>
Cheng applies this to unravel some of the currently hot topics that roam the media like (political) discussions about health care, or racism and sexism. She clearly explains why the different parties can not come to an agreement. People come to their own version of "The Truth" by making logical mistakes. For example a negation is mistaken for a contraposition, or they use a false premise which logically allows to imply anything, or people apply the rules to different classes of subjects, etc.</p>
<p>
To be able to point out where things go wrong in many practical situations, Cheng of course needs to explain some rules and terms form logic that are much more clearly defined in a mathematical situation. Mathematicians will agree on what is true or correct because they are arguing within a much more abstract and unambiguous universe, using generally accepted rules, even though they need not make all the details of their logical deduction steps explicit. As long as their peers will be able to see how the gaps need to be filled, they will accept the result. Only if the gaps are too large, a referee will require more details.</p>
<p>
So the first part of this book is explaining what logic actually is and how it is experienced every day by anyone. Using many examples from social discussions, political disagreement, or just parent-kid discussions, Chen introduces the different terms, using some necessary abstraction, to talk properly about the terms that are used in more formal proposition logic, including quantifiers, Venn diagrams, truth tables, negation of implications, equivalence, but also fuzzy logic (the world has many "grey zones"),... When there is a discussion about who is to blame for some unfortunate event, then one should first see how it is possible that the event came about, and those previous events are caused in turn by some other events, etc. So there can be a very complex network of causal coincidences that have eventually led to the event that is the subject of the dispute (Chen uses all these relations as a pretext to smuggle in some of her beloved category theory).</p>
<p>
In a second part she explains the limits of logic. In practice there is no peer reviewing process of some person's argument like in a mathematical environment of publishing a paper. Which mechanisms (correct or inappropriate) are used to convince people? Perhaps (Internet) memes are assumed correct while they are not. When one comes to paradoxes, some alarm should go off to revise the system applied. In other situations, logic will not be useful like in emergencies, or when we do not have all the information to act logically, in which cases we may perhaps just follow a reflex, a gut feeling, or trust the judgement of others.</p>
<p>
The third and last part is called beyond logic. This is where one should agree on axioms, the things that are accepted without a (logic) proof. Then there are of course the many grey zones where binary logic is not the proper tool to use. What universe is one talking about (all humans, all men, all women, all white women, all rich and white women,...?) Things may be considered equivalent (the same) for somebody, but not for the adversary. And then there are of coarse emotions that are important factors in everything we do or say.</p>
<p>
In this book Chen is strongly engaged in social justice, minority groups, gurus, religion, climate issues, the role of science, etc. So in her last chapter she somehow summarizes how logic can help you to be a reasonable and intelligent person. There should be some framework that one believes in, and one should be sceptical towards charismatic "superstars". You should realize that there are a lot of grey zones and that you are not alone so that reaching a joint objective can be more rewarding than reaching your own. Correct and reasonable logical arguments should be used, even in a world that is not always logical.</p>
<p>
This is an engaging book, that should be read by everyone. It will help solving disagreements, or direct discussions away from and "it is - it isn't" arguments, and help you focus on the underlying cause of the dispute. Of course real life is not mathematics, boundaries are fuzzy, and obviously, it can not prevent that people disagree, and they should if for the proper reasons and when using the correct arguments, and this is the main message of the book.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
In this book, Cheng illustrates how by using logic, one can become a better, reasonable, and intelligent human. She describes the possibilities, the limitations, and the pitfalls of logic when it is applied beyond the abstract context of mathematics. Can it define what is right or wrong or help to resolve a deadlock in political or social discussions about subjects such as solidarity principles, climate issues, racism, or sexism?</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/eugenia-cheng" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Eugenia Cheng</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/profile-books" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">profile books</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2019</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-1-78816038-4 (hbk); 978-1-78283442-7 (ebk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">£14.99 (hbk); £12.99 (ebk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">320</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="https://profilebooks.com/the-art-of-logic-hb.html" title="Link to web page">https://profilebooks.com/the-art-of-logic-hb.html</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00a06" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a06</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/03-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">03-01</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/97a40" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97a40</a></li><li class="vocabulary-links field-item even"><a href="/msc-full/00a09" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a09</a></li></ul></span>Thu, 03 Jan 2019 08:09:55 +0000Adhemar Bultheel48975 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/art-logic#commentsBeyond Infinity: An Expedition to the Outer Limits of Mathematics
https://euro-math-soc.eu/review/beyond-infinity-expedition-outer-limits-mathematics
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Eugenia Cheng is a professor of mathematics whose research field is higher dimensional category theory. She has made it one of her missions to counter mathphobia. Her credo is that mathematics is not the difficult part to deal with in life, but that on the contrary it is life that is difficult and mathematics helps us to make it simpler and manageable. She has tried to illustrate this by combining her love for cooking and her passion for mathematics in her previous book <em>Cakes, Custard + Category Theory</em> (reviewed <a href="/review/cakes-custard-category-theory" target="_blank">here</a>). In that book she gave attention to mathematics alright, but there were also proper recipes for cooking. The latter are interesting if you love cooking yourself and they are a springboard to make a link towards mathematics, but they do not really help to understand category theory.</p>
<p>
In the present book however she is explaining a really important mathematical concept: infinity, and it is far from being the simplest one to explain for non-mathematicians. The approach here is that she does just that. Not like in her previous book where she placed cookery next to the mathematics. Here of course Chen is still Chen and she still can't hide her love for cooking and category theory. However cooking is now only used as an anecdote or as and introduction to a chapter, just like perhaps a hiking experience, of a concert she attended, can be.</p>
<p>
So what is this book about? The first part is intended to explain what infinity really is, and it soon becomes clear that it is not as simple as saying it is larger than any number one can imagine. It cannot be a number since the usual arithmetic rules do not work as with finite numbers. And then there are the paradoxes like the well known Hilbert hotel with infinitely many rooms that can always accommodate infinitely many more guests, even when it is fully booked. So Chen uses a more systematic approach introducing the simplest number systems: natural numbers, integers, and rationals. She goes even further and defines the natural numbers in the set theoretic style of Frege, only she does not use the abstract concept of a set, but she uses 'bags' instead. So 0 corresponds to the empty bag, 1 to the bag containing only the empty bag, 2 to the bag containing the two previous bags, etc. Also concepts like injection, surjection, and countable are introduced here.</p>
<p>
Then a stumble stone is blocking the development. It turns out that there are more than countably many real numbers. The reals are not properly defined yet, but using Cantor's diagonal argument, and using a binary representation, Chen shows that there are more irrational numbers than natural numbers. Thus there are gradations of infinity, at which point $\aleph_0$ is introduced. The 'smallest' infinity of a countable set, but there exist higher forms like $\aleph_1=2^{\aleph_0}$ the number of reals, and this can be iterated $\aleph_k=2^{\aleph_{k-1}}$. The continuum hypothesis is briefly touched upon, and it is noted that it can't be proved (Cohen) or disproved (Gödel). The distinction between ordinal and cardinal numbers clarifies the difficulty that infinity gives with the usual arithmetic operations.</p>
<p>
All this work in the first part of the book, leading to an understanding of what infinity actually is, is like a journey uphill. In a second part Chen points to the sights that are possible from the top of the hill. With the recursive definition of the natural numbers, a proof by induction is within reach and one can solve all sorts of counting problems and even evaluate infinite sums. Although the latter needs more careful consideration. She also introduces higher dimensions, i.e., larger than 2 or 3. It may even grow to infinity for a continuum. When a relation or a property is associated with a dimension, this brings her to her beloved research subject: higher dimensional category theory. Perhaps, this doesn't fit so well in the otherwise rather elementary exposition, but it is a nice, be it a somewhat unusual example, of a higher dimensional mathematical object.</p>
<p>
The move is then from the infinitely large to the infinitely small, leading back to infinite sums of diminishing terms and Zeno paradoxes. What is needed here is the concept of a limit. She however explains it essentially avoiding to use that name. Instead she illustrates the idea with hitting a target that becomes smaller and smaller. This way it can be explained what infinitesimals are and how they are applied. It can now be proved that the harmonic series diverges, and eventually also that irrational numbers do exist, which is done by approaching Dedekind's definition of the reals.</p>
<p>
I find this a very pleasing way of introducing some elementary, but also some less elementary, mathematical concepts to the layperson. Taking infinity as the carrot to lead the reader uphill is an interesting choice. This is the most essential concept needed when moving from algebra to analysis. Chen is an excellent guide to show the reader the way uphill. With many analogies and illustrations and reformulations it seems like the reader is carried to the top, no toiling required. The story is told fluently. Side remarks, historical notes, or a slightly more advanced remark are inserted as a framed boxes in the text. I guess it will be too elementary for mathematicians of mathematics students, but it is warmly recommended for secondary school pupils. In fact anyone who has the slightest interest in what infinity actually means should read it. The word is used lightly in common language, but you will learn what it means in a more exact sense and thus what it means to a mathematician. It turns out that it triggered the development of calculus and it has shaken the foundations of mathematics as recently as in the early 20th century.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Eugenia Cheng continues her crusade against mathphobia. In this book she explores the meaning of infinity. To properly define infinity she has to define the cardinality of the natural numbers, and thus also the definition of the latter. That includes solving the inconsistencies with arithmetic operations and the paradoxes that result. However it turns out that the real numbers are not countable, so that there are gradations of infinity and hence also the definition of the reals is needed. That requires to consider the infinitely small, which leads to infinitesimals that form the onset of calculus. All is brought to the reader avoiding the usually boring technical approach of mathematics, but using many analogies and elementary everyday language.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/eugenia-cheng" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Eugenia Cheng</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/profile-books" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">profile books</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2017</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-1781252857 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">GBP 12.99 (pbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">316</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="https://profilebooks.com/beyond-infinity.html" title="Link to web page">https://profilebooks.com/beyond-infinity.html</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00-01</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00a09" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a09</a></li></ul></span>Thu, 20 Apr 2017 13:12:50 +0000Adhemar Bultheel47634 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/beyond-infinity-expedition-outer-limits-mathematics#commentsCakes, Custard + Category Theory
https://euro-math-soc.eu/review/cakes-custard-category-theory
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Eugenia Cheng is a senior mathematics lecturer at Sheffield University (UK) whose domain is higher-dimensional category theory. She has gained some popularity from her YouTube videos where she mixes her love for cooking and for mathematics to show the analogy between both and to show that knowledge of one can help understanding the other. This is exactly what she also wants to achieve in this book as the subtitle promises: <em>Easy recipes for understanding complex maths</em>. She is also active as a pianist, but that is not used much in this context. This illustrates that she is a very enthusiast communicative and talkative ambassador for the popularization of mathematics. She definitely wants to convince people that it is not mathematics that is difficult, but that it is life that is complicated and mathematics is just there to simplify it and make it much easier to solve problems.</p>
<p>
In this book she engages in the task to explain what category theory is to mathematical lay people, which is certainly not an easy or obvious choice. I doubt that a mathematical illiterate after reading the book will be able to tell you what category theory really is. But they will have gotten at least a vague idea. Fortunately, Cheng starts from scratch and is meandering along many other topics along the way. In fact, there are two parts: the first explains what mathematics is about, and the second part explains what category theory is: the mathematics of mathematics. The two parts are not much different. Cheng is following the mathematical river of concepts flowing to its estuary of understanding. She also tells about the many brooks, streamlets, and bourns that feed it. The recipes that she starts each chapter with, are not really essential in my opinion. Of course cookery programs are currently very popular and it is a kind of a opening sentence to start a discussion about something that really matters. The recipes sum up the ingredients and give a brief description of the method, and you will get some ideas of how to deal with certain allergies in your cooking, but I believe you should know something about cooking if you want to really use them since not many details are given. More or less the same holds for the mathematics. The most elementary topics of mathematics are explained, but it is advisable that you know a bit of mathematics to keep apace with Cheng. You do learn that the concept of a number is not that obvious, you learn about logic, what a proof is, how one arrives at an axiomatic system by repeatedly asking `why?', you learn about complex numbers, and a group, about the unsuccessful attempts to prove the fifth axiom of Euclidean geometry, you are convinced that distance is not always the same as a Euclidean distance, and you are introduced to topology. That's a whole lot if you only have secondary school mathematics in you backpack, and certainly if it has been a while since you needed it. All this is wrapped up in much story telling featuring Fermat, Poincaré, and Riemann, and a lot of foody and cookery stuff. And this is just the mathematics part.</p>
<p>
In the category part, relations (morphisms) represented as arrows connecting objects become important. The example of genetic and mathematical family ties (e.g. the Erdős number), are examples. It is all about structures and removing as much as possible to keep the simplest skeleton. Some of the properties of the mappings are explained and simple examples are given, but a clear and strict axiomatic definition is not really given. However you learn about what it can mean to say that structures are `the same', what a monoid or a universal property is, and even what a colimit is. And again the wrapping consists of many stories e.g. about Nelson's last message to his fleet before the battle of Trafalgar, the three domes of St. Paul's Cathedral and Battenberg cakes. I find the discussion in the concluding chapter about truth most interesting. It is about different gradations or meanings of `truth' depending on (1) what we know, (2) what we understand, and (3) what we believe. The most `secure' truth is what is in the intersection of the three.</p>
<p>
The enthusiasm of Cheng is contagious, and she knows how to take the reader along on her hiking tour (not really a stroll in the park). Do not expect that after reading the book you will be ready to start reading current research in category theory. Even the reader that is a mathematician may be somewhat confused because it is too different from the top-down axiomatic and much less verbose books that he probably is more used to. But I do not think professional mathematicians are the first targets that Cheng had in mind when writing this book. Nevertheless, it is entertaining reading stuff that the professional and the non-professional will appreciate.</p>
<p>
To avoid some confusion, let me finally point out that this book is published in UK by Profile Books, but that the same book is available in the US under a different title <em>How to bake pi: an edible exploration of the mathematics of mathematics</em> published by Basic Books.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is a brave attempt to show us that mathematics is there to make our lives easy and not the other way around. Cheng does not use applied mathematics to convince the reader, but instead explains the layman what category theory, her own research field, is about, and how it simplifies structures to their bare minimum, so that the proof of a certain property still holds.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/eugenia-cheng" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Eugenia Cheng</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/profile-books" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">profile books</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2015</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-1-781-25287-1 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">£ 12.99</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">302</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/algebra" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Algebra</a></li><li class="vocabulary-links field-item odd"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://www.profilebooks.com/isbn/9781781252871/" title="Link to web page">http://www.profilebooks.com/isbn/9781781252871/</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/18-category-theory-homological-algebra" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">18 Category theory, homological algebra</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/18-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">18-01</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/97-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97-01</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/97a80" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97A80</a></li></ul></span>Sat, 20 Jun 2015 07:33:51 +0000Adhemar Bultheel46268 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/cakes-custard-category-theory#comments