nLab base of enrichment




In enriched category theory, a base of enrichment is some kind of category theoretic structure VV – most often a monoidal category, but potentially something more general like a bicategory, virtual double category, or skew-monoidal category – over which one intends to consider VV-enriched categories.

Frequently, but not always, VV will be a Bénabou cosmos, which provides sufficient infrastructure to carry out enriched versions of most of the standard category theoretic constructions, for example of enriched functor categories, tensor products of enriched categories, enriched presheaf categories, Eilenberg-Moore categories, specific weighted limits and weighted colimits, and so on.

In this context, “change of base” or “change of base of enrichment”, refers to a 2-functor V-CatW-CatV\text{-}Cat \longrightarrow W\text{-}Cat between (very large) categories of enriched categories that is induced by a lax monoidal functor VWV \to W between bases of enrichment. See also the section Base change at enriched category.


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