コンマ圏
summary.icon
definition.icon コンマ圏$ F_0↓F_1 = \left\lang\textrm{Comma\ cat.}\colon C_0, D_0, C_1; F_0, F_1 \right\rang where
$ F_0\colon C_0 → D
$ F_1\colon C_1 → D
対象
$ \left\lang c_0, c_1; f \right\rang
where
$ c_0 \colon C_0
$ c_1 \colon C_1
$ f \colon c_0.F_0 → c_1.F_1 \colon D
射
$ \left\lang g_0, g_1 \right\rang \colon \left\lang c_0, c_1; f \right\rang → \left\lang c_0', c_1'; f' \right\rang
where
$ g_0\colon c_0 → c_0'
$ g_1\colon c_1 → c_1'
s.t.
$ f\mathbin{;}g_1.F_1 = g_0.F_0 \mathbin{;}f'