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Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.inv_whiskerLeft

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] (X : C) {Y Z : C}
  (f : Y ⟶ Z) [inst_2 : CategoryTheory.IsIso f],
  CategoryTheory.inv (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X f) =
    CategoryTheory.MonoidalCategoryStruct.whiskerLeft X (CategoryTheory.inv f)
Defined in
Mathlib.CategoryTheory.Monoidal.Category
Cited by
10 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.IsIso

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_inv · cited by 8MonoidalCategory.whiskerL…CategoryTheory.MonoidalCategory.pentagon_inv · cited by 4MonoidalCategory.pentagon…CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_inv_hom · cited by 2MonoidalCategory.pentagon…CategoryTheory.BraidedCategory.braiding_tensor_left_inv · cited by 2BraidedCategory.braiding_…CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_inv · cited by 2MonoidalCategory.pentagon…CategoryTheory.BraidedCategory.braiding_tensor_right_inv · cited by 2BraidedCategory.braiding_…CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_inv_inv · cited by 2MonoidalCategory.pentagon…CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_hom_hom · cited by 1MonoidalCategory.pentagon…CategoryTheory.SymmetricCategory.tensorμ_braid_swap · cited by 1SymmetricCategory.tensorμ…CategoryTheory.MonoidalCategory.inv_tensor · cited by 0MonoidalCategory.inv_tens…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.MonoidalCategoryStruct.tensorObj · cited by 3106MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.IsIso · cited by 1156CategoryTheory.IsIsoCategoryTheory.MonoidalCategoryStruct.whiskerLeft · cited by 915MonoidalCategoryStruct.wh…CategoryTheory.inv · cited by 467CategoryTheory.invCategoryTheory.IsIso.inv_eq_of_hom_inv_id · cited by 24IsIso.inv_eq_of_hom_inv_idCategoryTheory.MonoidalCategory.whiskerLeft_hom_inv' · cited by 2MonoidalCategory.whiskerL…MonoidalCategory.inv_whiskerL…CITED BYCITES

Cites10

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Cited by10

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