Let C and A be categories, and let ~ be a congruence on C. If T: C to A is afunctor with T(f) = T(g) whenever f ~ g, then T defines a functor T': C' to A(where C' is the quotient category) by T'(X) =...

Let C and A be categories, and let ~ be a congruence on C. If T: C to A is afunctor with T(f) = T(g) whenever f ~ g, then T defines a functor T': C' to A(where C' is the quotient category) by T'(X) = T(X) for every object X andT'([f]) = T(f) for every morphism f.