[Merged by Bors] - chore(CategoryTheory): generalize universes for WellPowered#19992
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[Merged by Bors] - chore(CategoryTheory): generalize universes for WellPowered#19992
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PR summary c0f67bf368Import changes for modified filesNo significant changes to the import graph Import changes for all files
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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.
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If
C : Type uandCategory.{v} C, we generalizeWellPowered Cby introducing an auxiliary universew. The categoryCsatisfiesWellPowered.{w} Cnow if it is locally small relative towand the type of subobjects of anyX : Cisw-small. The previous definition corresponds to the casew = v.It was necessary to introduce a new file
CategoryTheory.Comma.LocallySmall: it contains variousLocallySmallinstances for categories likeComma,StructuredArrow,Over, etc.Apart from this, the only "new" result is a
WellPowered.{w} Cinstance for abelian categories satisfyingIsGrothendieckAbelian.{w} C.This generalization of
WellPoweredis used in #20014.