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diagonal_functor [2014/09/26 15:10] nikolaj |
diagonal_functor [2014/12/04 22:35] nikolaj |
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| | @#55CCEE: context | @#55CCEE: ${\bf C},{\bf D}$ ... category | | | @#55CCEE: context | @#55CCEE: ${\bf C},{\bf D}$ ... category | | ||
| | @#FFBB00: definiendum | @#FFBB00: $\Delta:{\bf C}\longrightarrow{\bf C}^{\bf D}$ | | | @#FFBB00: definiendum | @#FFBB00: $\Delta:{\bf C}\longrightarrow{\bf C}^{\bf D}$ | | ||
| - | | @#FF9944: definition | @#FF9944: $\Delta\,C:=\Delta_C$ | | + | | @#FF9944: definition | @#FF9944: $\Delta C:=\Delta_C$ | |
| | @#FF9944: definition | @#FF9944: $\Delta(f):=\mathrm{const}_f$ | | | @#FF9944: definition | @#FF9944: $\Delta(f):=\mathrm{const}_f$ | | ||
| ==== Discussion ==== | ==== Discussion ==== | ||
| + | === Coherence === | ||
| + | Note that for constant functors $\Delta_A,\Delta_B$, the square in the definition of a natural transformation commutes trivially. Hence any arrow $f:{\bf C}[A,B]$ gives rise to a natural transformation. | ||
| + | |||
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Diagonal_functor|Diagonal functor]] | Wikipedia: [[http://en.wikipedia.org/wiki/Diagonal_functor|Diagonal functor]] | ||
| Line 14: | Line 17: | ||
| ==== Parents ==== | ==== Parents ==== | ||
| === Context === | === Context === | ||
| - | [[Category]] | + | [[Categories]] |
| === Element of === | === Element of === | ||
| [[Functor]] | [[Functor]] | ||
| === Requirements === | === Requirements === | ||
| [[Constant functor]], [[Functor category]] | [[Constant functor]], [[Functor category]] | ||
