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The book presents aspects of homological algebra in functor categories, with emphasis on polynomial functors between vector spaces over a finite field. With these foundations in place, the book presents applications to representation theory, algebraic topology and K-theory. As these applications reveal, functor categories offer powerful computational techniques and theoretical insights.
T. Pirashvili sets the stage with a discussion of foundations. E. Friedlander then presents applications to the rational representations of general linear groups. L. Schwartz emphasizes the relation of functor categories to the Steenrod algebra. Finally, V. Franjou and T. Pirashivili present A. Scorichenko's understanding of the stable K-theory of rings as functor homology.