  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.
