comma category

Noun

 * 1)  A category built out of a pair of functors that have the same codomain.
 * 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 $$T(g)$$.

Translations

 * German: Kommakategorie
 * Korean: 쉼표 범주
 * Russian: категория запятой
 * Spanish: categoría coma