In this paper, we define the functor category Fquad associated to F2-vector spaces equipped with a quadratic form. We show the existence of a fully faithful, exact functor ι : F → Fquad, which preserves simple objects, where F is the category of functors from the category of finite-dimensional F2-vector spaces to the category of all F2-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 κ : Fiso → Fquad which preserves simple objects. © 2007 Elsevier Ltd. All rights reserved.
Vespa, C. (2008). Generic representations of orthogonal groups: The functor category Fquad. Journal of Pure and Applied Algebra, 212(6), 1472–1499. https://doi.org/10.1016/j.jpaa.2007.10.014