Commit 2021-05-01 00:19 b88a9d14
View on Github →feat(category_theory/enriched): abstract enriched categories (#7175)
Enriched categories
We set up the basic theory of V-enriched categories,
for V an arbitrary monoidal category.
We do not assume here that V is a concrete category,
so there does not need to be a "honest" underlying category!
Use X ⟶[V] Y to obtain the V object of morphisms from X to Y.
This file contains the definitions of V-enriched categories and
V-functors.
We don't yet define the V-object of natural transformations
between a pair of V-functors (this requires limits in V),
but we do provide a presheaf isomorphic to the Yoneda embedding of this object.
We verify that when V = Type v, all these notion reduce to the usual ones.