Let V denote a vector space over a finite field k and let Gr(V) be the Grassmannian of subspaces in V. Basic objects of study in this book are various categories of functors (called grassmannian functor categories) from the category of couples (V,W), where W belongs to Gr(V), to the category ₣ of vector spaces over k. The book contains a study of finite objects in these categories and their homological properties. General vanishing properties are proved, together with an application of grassmannian functor categories to the Krull filtration of the category of functors of the category ₣. Special attention is given to the case of the basic field k with two elements (in this case it is possible to prove Noetherian properties of studied functors).

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