On functors between categories with colored morphisms

Abstract

In this paper, we consider categories with colored morphisms and functors such that morphisms assigned to morphisms with a common color have a common color. In this paper, we construct a morphism-colored functor such that any morphismcolored functor from a given small morphism-colored groupoid to any discrete morphism-colored category factors through it. We also apply the main result to a schemoid constructed from a Hamming scheme.

A topos associated with a colored category

“…Tameness and naturality of a schemoid are described in terms of a coloring map used in [17]; see Appendix B.…”

“…In this section, we rewrite certain of the definitions described in the body of the manuscript with terminology which is used in [17] for considering a colored category. Such descriptions may yield a topos taking the place of the functor category Mod (C,S) in the study of schemoids; see Remark 5.7 (ii).…”