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Representable enriched functor
Definition
Let be a -category and assume is enriched in itself as in A closed monoidal category is enriched in itself. Fix an object of .
The representable enriched functor
is the -functor whose value at is the hom-object and whose structure morphism on a pair is the transpose, in the self-enrichment of , of the enriched composition morphism
The contravariant representable is defined analogously on .
Depends on
Used by
- The enriched Yoneda assignment is fully faithful Corollary
- A V-category is tensored exactly when each covariant hom has a left enriched adjoint Theorem
- Every enriched functor into the base is a weighted colimit of representables when the displayed weighted colimit exists Theorem
- Weak enriched Yoneda lemma Theorem
Dependency tree · two levels
6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- G. M. Kelly, Basic Concepts of Enriched Category Theory, Section 1.6 and Section 1.10 (standard reference, not scraped)