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[Merged by Bors] - chore(CategoryTheory/EssentiallySmall): lower priority of the Category (Shrink C) instance #42981

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[Merged by Bors] - chore(CategoryTheory/EssentiallySmall): lower priority of the Category (Shrink C) instance #42981

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5 changes: 4 additions & 1 deletion Mathlib/CategoryTheory/EssentiallySmall.lean
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Expand Up @@ -206,7 +206,10 @@ end ShrinkHoms

namespace Shrink

noncomputable instance [Small.{w} C] : Category.{v} (Shrink.{w} C) :=
/- The priority is lower than that of `Preorder.smallCategory`: when `C` is a small preorder,
`Shrink.{w} C` then gets its category structure from `Preorder (Shrink.{w} C)`
(see `Mathlib/Order/Shrink.lean`), with morphisms in `Type w` rather than in `Type v`. -/
noncomputable instance (priority := 50) [Small.{w} C] : Category.{v} (Shrink.{w} C) :=
inferInstanceAs (Category (InducedCategory _ (equivShrink C).symm))

/-- The categorical equivalence between `C` and `Shrink C`, when `C` is small. -/
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