Differences
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natural_transformation [2014/12/03 23:00] nikolaj |
natural_transformation [2016/04/09 14:37] nikolaj |
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| ==== Collection ==== | ==== Collection ==== | ||
| | @#55CCEE: context | @#55CCEE: $F,G$ in ${\bf C}\longrightarrow{\bf D}$ | | | @#55CCEE: context | @#55CCEE: $F,G$ in ${\bf C}\longrightarrow{\bf D}$ | | ||
| - | | @#FFBB00: definiendum | @#FFBB00: $\eta$ in $\mathrm{nat}(F,G)$ | | + | | @#FFBB00: definiendum | @#FFBB00: $\eta$ in $F\xrightarrow{\bullet}G$ | |
| | @#AAFFAA: inclusion | @#AAFFAA: $\eta:{\large\prod}_{(A:\mathrm{Ob}_{\bf C})}F\,A\to G\,A$ | | | @#AAFFAA: inclusion | @#AAFFAA: $\eta:{\large\prod}_{(A:\mathrm{Ob}_{\bf C})}F\,A\to G\,A$ | | ||
| | @#55EE55: postulate | @#55EE55: @#88DDEE: $\eta\circ F(\,f)=G(\,f)\circ\eta$ | | | @#55EE55: postulate | @#55EE55: @#88DDEE: $\eta\circ F(\,f)=G(\,f)\circ\eta$ | | ||
| + | Here, in the postulate, I've left the components ($\eta_A,\eta B$ etc.) implicit. | ||
| ==== Discussion ==== | ==== Discussion ==== | ||
| === Idea === | === Idea === | ||
