Commit 2024-12-23 08:45 e258ed24
View on Github →chore(CategoryTheory): generalize universes for WellPowered (#19992)
If C : Type u
and Category.{v} C
, we generalize WellPowered C
by introducing an auxiliary universe w
. The category C
satisfies WellPowered.{w} C
now if it is locally small relative to w
and the type of subobjects of any X : C
is w
-small. The previous definition corresponds to the case w = v
.
It was necessary to introduce a new file CategoryTheory.Comma.LocallySmall
: it contains various LocallySmall
instances for categories like Comma
, StructuredArrow
, Over
, etc.
Apart from this, the only "new" result is a WellPowered.{w} C
instance for abelian categories satisfying IsGrothendieckAbelian.{w} C
.
This generalization of WellPowered
is used in #20014.