Diagonal functor

Functor

context ${\bf C},{\bf D}$ … category
definiendum $\Delta:{\bf C}\longrightarrow{\bf C}^{\bf D}$
definition $\Delta C:=\Delta_C$
definition $\Delta(f):=\mathrm{const}_f$

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

Parents

Context

Element of

Requirements

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