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In this paper, we consider categories with colored morphisms and functorssuch that morphisms assigned to morphisms with a common color have a commoncolor. In this paper, we construct a morphism-colored functor such that anymorphism-colored functor from a given small morphism-colored groupoid to anydiscrete morphism-colored category factors through it. We also apply the mainresult to a schemoid constructed from a Hamming scheme.

On functors between categories with colored morphisms