2016/11/22 by Katsuhiko Kuribayashi, Kuribayashi, Katsuhiko, Yasuhiude Numata +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1611.07246
openalex publication_date 2016/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that a functor category whose domain is a colored category is a topos.The topos structure enables us to introduce cohomology of colored categories including quasi-schemoids. If the given colored category arises from an association scheme, then the cohomology coincides with the group cohomology of the factor scheme by the thin residue. Moreover, it is shown that the cohomology of a colored category relates to the standard representation of an association scheme via the Leray spectral sequence.