The functor category Fquad

Details The functor category Fquad The functor category Fquad

2006-06-20

arxiv.org/abs/math/0606484v1

Mathematics

Algebraic Topology

26 pages

Scientific paper

In this paper, we define the functor category Fquad associated to vector spaces over the field with two elements, F\_2, equipped with a quadratic form. We show the existence of a fully-faithful, exact functor \iota: \F \to Fquad, which preserves simple objects, where \F is the category of functors from the category of finite dimensional F\_2-vector spaces to the category of all F\_2-vector spaces. We define the subcategory Fiso of Fquad, which is equivalent to the product of the categories of modules over the orthogonal groups; the inclusion is a fully-faithful functor \kappa: Fiso \to Fquad which preserves simple objects.

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