2006/06/20 by Christine Vespa, Vespa, Christine
Mathematics · #16D90 #18A25 #20C20 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.AT #math.RT #msc:16D90 #msc:18A25 #msc:20C20
paper · pdf · doi:10.48550/arxiv.math/0606484
26 pages
arxiv created 2006/06/20 · openalex publication_date 2006/06/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ι: \F → 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 κ: Fiso → Fquad which preserves simple objects.