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101damnations
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Mathlib/CategoryTheory/Action/Basic.lean

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@@ -334,13 +334,13 @@ def resComp {G H K : Type u} [Monoid G] [Monoid H] [Monoid K]
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-- TODO promote `res` to a pseudofunctor from
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-- the locally discrete bicategory constructed from `Monᵒᵖ` to `Cat`, sending `G` to `Action V G`.
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variable {G H : MonCat.{u}} (f : G H)
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variable {G H : Type u} [Monoid G] [Monoid H] (f : G →* H)
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/-- The functor from `Action V H` to `Action V G` induced by a morphism `f : G → H` is faithful. -/
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instance : (res V f).Faithful where
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map_injective {X} {Y} g₁ g₂ h := by
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ext
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rw [← res_map_hom _ _ g₁, ← res_map_hom _ _ g₂, h]
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rw [← res_map_hom _ f g₁, ← res_map_hom _ f g₂, h]
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/-- The functor from `Action V H` to `Action V G` induced by a morphism `f : G → H` is full
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if `f` is surjective. -/

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