comma category
noun1
Category theory, Computing, Engineering, Mathematics, Natural sciences, Physical sciences, Sciences A category built out of a pair of functors that have the same codomain.
- Given a pair of functors S:𝒜→𝒞 and T:ℬ→𝒞, objects of the comma category S↓T are arrows h:S(A)→T(B) parametrized by triples (A, B, h), and given morphisms f:A→A' and g:B→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')→T(B') and from S(f) to T(g).
- Hyponyms
- arrow category, slice category, coslice category