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feat(category_theory): every category is essentially small... (#15874)
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...if you look at it from far enough away.
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TwoFX committed Aug 10, 2022
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Expand Up @@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import logic.small
import category_theory.category.ulift
import category_theory.skeletal

/-!
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essentially_small.{w} (discrete α) :=
⟨⟨discrete (shrink α), ⟨infer_instance, ⟨discrete.equivalence (equiv_shrink _)⟩⟩⟩⟩

lemma essentially_small_self : essentially_small.{max w v u} C :=
essentially_small.mk' (as_small.equiv : C ≌ as_small.{w} C)

/--
A category is `w`-locally small if every hom set is `w`-small.
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