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

Wikipedia: Diagonal functor

nLab: Diagonal functor

Parents

Context

Element of

Functor

Requirements

Constant functor, Functor category

Diagonal functor

Functor

Discussion

Coherence

Reference

Parents

Context

Element of

Requirements

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Improvements of the human condition

Diagonal functor

Functor

Discussion

Coherence

Reference

Parents

Context

Element of

Requirements

Search

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Improvements of the human condition