On functors between categories with colored morphisms

TL;DR

This paper studies functors between categories with colored morphisms, constructing a universal morphism-colored functor and applying it to a schemoid derived from a Hamming scheme.

Contribution

It introduces a universal morphism-colored functor for categories with colored morphisms and demonstrates its application to schemoids from Hamming schemes.

Findings

Constructed a universal morphism-colored functor.

Showed factorization property for morphism-colored functors.

Applied the theory to a schemoid from a Hamming scheme.

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 morphism-colored 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.