===== Diagonal functor =====
==== Functor ====
| @#55CCEE: context     | @#55CCEE: ${\bf C},{\bf D}$ ... category |
| @#FFBB00: definiendum | @#FFBB00: $\Delta:{\bf C}\longrightarrow{\bf C}^{\bf D}$ |
| @#FF9944: definition  | @#FF9944: $\Delta C:=\Delta_C$ |
| @#FF9944: definition  | @#FF9944: $\Delta(f):=\mathrm{const}_f$ |

==== 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 ===
Wikipedia: [[http://en.wikipedia.org/wiki/Diagonal_functor|Diagonal functor]]

nLab: [[http://ncatlab.org/nlab/show/diagonal+functor|Diagonal functor]]

==== Parents ====
=== Context ===
[[Categories]]
=== Element of ===
[[Functor]]
=== Requirements ===
[[Constant functor]], [[Functor category]]