豐饒圈
enriched category
$ a\in|{\bf C}|を對象と言ふ
任意の對象$ a,b\in|{\bf C}|に對して$ {\bf C}(a,b)\in|{\bf M}|を對應させて、$ {\bf C}(a,b)を$ aから$ bへの射の類 (class)と言ふ 任意の對象$ a,b,c\in|{\bf C}|に對して、以下の可換圖式を滿たす$ \circ_{abc}:{\bf C}(b,c)\otimes{\bf C}(a,b)\to{\bf C}(a,c)を合成射 (反圖式順) と言ふ $ ({\bf C}(c,d)\otimes{\bf C}(b,c))\otimes{\bf C}(a,b)\xrightarrow{\alpha}{\bf C}(c,d)\otimes({\bf C}(b,c)\otimes{\bf C}(a,b))\xrightarrow{1\otimes\circ_{abc}}{\bf C}(c,d)\otimes{\bf C}(a,c)\xrightarrow{\circ{acd}}{\bf C}(a,d)\xleftarrow{\circ_{abd}}{\bf C}(b,d)\otimes{\bf C}(a,b)\xleftarrow{\circ_{bcd}\otimes 1}({\bf C}(c,d)\otimes{\bf C}(b,c))\otimes{\bf C}(a,b)
任意の對象$ a\in|{\bf C}|に對して、以下の可換圖式を滿たす$ {\rm id}_a:I\to{\bf C}(a,a)を$ aの恆等射と言ふ $ I\otimes{\bf C}(a,b)\xrightarrow{\lambda}{\bf C}(a,b)\xleftarrow{\circ_{abb}}{\bf C}(b,b)\otimes{\bf C}(a,b)\xleftarrow{{\rm id}_b\otimes 1}I\otimes{\bf C}(a,b)
$ {\bf C}(a,b)\otimes I\xrightarrow{\rho}{\bf C}(a,b)\xleftarrow{\circ_{aab}}{\bf C}(b,b)\otimes{\bf C}(a,b)\xleftarrow{1\otimes{\rm id}_b}{\bf C}(a,b)\otimes I