Colimit of a parallel pair f, g : A ⇒ B: the universal object Q with q: B → Q such that qf = qg. In Set it is B/~ where ~ is the equivalence relation generated by f(a) ~ g(a). In an abelian category: coeq(f,g) = coker(f − g).
Colimit of a parallel pair f, g : A ⇒ B: the universal object Q with q: B → Q such that qf = qg. In Set it is B/~ where ~ is the equivalence relation generated by f(a) ~ g(a). In an abelian category: coeq(f,g) = coker(f − g).