Theorems · Theorem · category theory

CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_X_obj

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  [inst_2 : CategoryTheory.MonoidalCategory D] [inst_3 : CategoryTheory.BraidedCategory D]
  (F : CategoryTheory.Functor C (CategoryTheory.CommMon D)) (X : C),
  (CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse.obj F).X.obj X = (F.obj X).X

Defined in: Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory
Cited by: 0 results in Mathlib
Foundations: Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.MonoidalCategory CategoryTheory.BraidedCategory

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.BraidedCategorystatement and proof · cited by 779
CategoryTheory.CommMonstatement and proof · cited by 85
CategoryTheory.CommMon.Xstatement and proof · cited by 50
CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inversestatement and proof · cited by 12

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