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.