comma category

English

Noun

comma category (plural comma categories)

1. (category theory) 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 $T(g)$.

Hyponyms

• arrow category
• slice category
• coslice category

Translations

Translations

• German: Kommakategorie
• Korean: 쉼표 범주 (swimpyo beomju)
• Russian: категория запятой (kategorija zapjatoj)
• Spanish: categoría coma