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Question: Can the following basic fact be conveniently cited from the literature?
For
a (co)complete symmetric closed monoidal category
a -enriched and -(co)tensored closed monoidal category
a small -enriched category
then the -enriched functor category is -enriched and -(co)-tensored:
The tensoring is objectwise over the tensoring of over
the enrichement (powering) is objectwise an end over hom- (power-) objects into the codomain object out of the tensoring of the domain with the corresponding representable.
This follows via standard end-yoga, I may spell it out in the nLab entry later. But what I’d like to know is if there is an existing textbook or other publication that makes this explicit?
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