A topos associated with a colored category

摘要

We show that a functor category whose domain is a colored category is atopos.The topos structure enables us to introduce cohomology of coloredcategories including quasi-schemoids. If the given colored category arises froman association scheme, then the cohomology coincides with the group cohomologyof the factor scheme by the thin residue. Moreover, it is shown that thecohomology of a colored category relates to the standard representation of anassociation scheme via the Leray spectral sequence.