About: Given a pair of functors S: \mathcal{A} \rightarrow \mathcal{C} and T: \mathcal{B} \rightarrow \mathcal{C}, objects of the comma category S \downarrow T are arrows h: S(A) \rightarrow T(B) parametrized by triples (A, B, h), and given morphisms f : A \rightarrow A' and g : B \rightarrow B', then a morphism of the said comma category is a commuting square parametrized by the pair (f, g) and spanning the area from h to h' : S(A') \rightarrow T(B') and from S(f) to T(g).       Sponge   NotDistinct   Permalink