Comma category

English

Noun

1. Template:Lb A category built out of a pair of functors that have the same codomain.

   Given a pair of functors $S:𝒜\to 𝒞$ and $T:ℬ\to 𝒞$, objects of the comma category $S\downarrow T$ are arrows $h:S(A)\to T(B)$ parametrized by triples (A, B, h), and given morphisms $f:A\to A^{\prime }$ and $g:B\to B^{\prime }$, 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 $h^{\prime }:S(A^{\prime })\to T(B^{\prime })$ and from $S(f)$ to $T(g)$.

Hyponyms

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Translations

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