@@ -66,7 +66,7 @@ structure Hom (A B : AlgebraCat.{v} R) where
6666instance : Category (AlgebraCat.{v} R) where
6767 Hom A B := Hom A B
6868 id A := ⟨AlgHom.id R A⟩
69- comp f g := ⟨g.algHom .comp f.algHom ⟩
69+ comp f g := ⟨g.hom .comp f.hom ⟩
7070
7171instance {M N : AlgebraCat.{v} R } : CoeFun (M ⟶ N) (fun _ ↦ M → N) where
7272 coe f := f.hom
@@ -130,7 +130,7 @@ instance : Inhabited (AlgebraCat R) :=
130130instance : ConcreteCategory.{v} (AlgebraCat.{v} R) where
131131 forget :=
132132 { obj := fun R => R
133- map := fun f => f.algHom }
133+ map := fun f => f.hom }
134134 forget_faithful := ⟨fun h => by ext x; simpa using congrFun h x⟩
135135
136136lemma forget_obj {A : AlgebraCat.{v} R} : (forget (AlgebraCat.{v} R)).obj A = A := rfl
@@ -148,12 +148,12 @@ instance {S : AlgebraCat.{v} R} : Algebra R ((forget (AlgebraCat R)).obj S) :=
148148instance hasForgetToRing : HasForget₂ (AlgebraCat.{v} R) RingCat.{v} where
149149 forget₂ :=
150150 { obj := fun A => RingCat.of A
151- map := fun f => RingCat.ofHom f.algHom .toRingHom }
151+ map := fun f => RingCat.ofHom f.hom .toRingHom }
152152
153153instance hasForgetToModule : HasForget₂ (AlgebraCat.{v} R) (ModuleCat.{v} R) where
154154 forget₂ :=
155155 { obj := fun M => ModuleCat.of R M
156- map := fun f => ModuleCat.asHom f.algHom .toLinearMap }
156+ map := fun f => ModuleCat.asHom f.hom .toLinearMap }
157157
158158@[simp]
159159lemma forget₂_module_obj (X : AlgebraCat.{v} R) :
@@ -183,7 +183,7 @@ def free : Type u ⥤ AlgebraCat.{u} R where
183183def adj : free.{u} R ⊣ forget (AlgebraCat.{u} R) :=
184184 Adjunction.mkOfHomEquiv
185185 { homEquiv := fun _ _ =>
186- { toFun := fun f ↦ (FreeAlgebra.lift _).symm f.algHom
186+ { toFun := fun f ↦ (FreeAlgebra.lift _).symm f.hom
187187 invFun := fun f ↦ ofHom <| (FreeAlgebra.lift _) f
188188 left_inv := fun f ↦ by aesop
189189 right_inv := fun f ↦ by simp [forget_obj, forget_map] } }
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