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Mathlib.CategoryTheory.ConcreteCategory.ReflectsIso

A forget₂ C D forgetful functor between concrete categories C and D whose forgetful functors both reflect isomorphisms, itself reflects isomorphisms.

theorem CategoryTheory.reflectsIsomorphisms_forget₂ (C : Type (u + 1)) [Category.{v_1, u + 1} C] {FC : outParam (CCType u)} {CC : outParam (CType u)} [outParam ((X Y : C) → FunLike (FC X Y) (CC X) (CC Y))] [ConcreteCategory C FC] (D : Type (u + 1)) [Category.{v_2, u + 1} D] {FD : outParam (DDType u)} {CD : outParam (DType u)} [outParam ((X Y : D) → FunLike (FD X Y) (CD X) (CD Y))] [ConcreteCategory D FD] [HasForget₂ C D] [(forget C).ReflectsIsomorphisms] :

A forget₂ C D forgetful functor between concrete categories C and D where forget C reflects isomorphisms, itself reflects isomorphisms.