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Mathlib/CategoryTheory/Monoidal Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -723,19 +723,13 @@ theorem whiskerLeft_id_bimod {X Y Z : Mon C} {M : Bimod X Y} {N : Bimod Y Z} :
723723 whiskerLeft M (𝟙 N) = 𝟙 (M.tensorBimod N) := by
724724 ext
725725 apply Limits.coequalizer.hom_ext
726- dsimp only [tensorBimod_X, whiskerLeft_hom, id_hom']
727- simp only [whiskerLeft_id, ι_colimMap, parallelPair_obj_one,
728- parallelPairHom_app_one, Category.id_comp]
729- erw [Category.comp_id]
726+ simp [TensorBimod.X]
730727
731728theorem id_whiskerRight_bimod {X Y Z : Mon C} {M : Bimod X Y} {N : Bimod Y Z} :
732729 whiskerRight (𝟙 M) N = 𝟙 (M.tensorBimod N) := by
733730 ext
734731 apply Limits.coequalizer.hom_ext
735- dsimp only [tensorBimod_X, whiskerRight_hom, id_hom']
736- simp only [id_whiskerRight, ι_colimMap, parallelPair_obj_one,
737- parallelPairHom_app_one, Category.id_comp]
738- erw [Category.comp_id]
732+ simp [TensorBimod.X]
739733
740734theorem whiskerLeft_comp_bimod {X Y Z : Mon C} (M : Bimod X Y) {N P Q : Bimod Y Z} (f : N ⟶ P)
741735 (g : P ⟶ Q) : whiskerLeft M (f ≫ g) = whiskerLeft M f ≫ whiskerLeft M g := by
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