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Theorems · Theorem · category theory

CategoryTheory.IsIso.Iso.inv_hom

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ≅ Y), CategoryTheory.inv f.hom = f.inv
Defined in
Mathlib.CategoryTheory.Iso
Cited by
18 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

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

CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_inv · cited by 8MonoidalCategory.whiskerL…CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv · cited by 7Bicategory.whiskerLeft_ri…CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom · cited by 3StrongTrans.naturality_na…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.Functor.congr_inv_of_congr_hom · cited by 1Functor.congr_inv_of_cong…CategoryTheory.Bicategory.pentagon_inv_inv_hom_inv_inv · cited by 1Bicategory.pentagon_inv_i…CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_hom_hom · cited by 1MonoidalCategory.pentagon…CategoryTheory.Bicategory.pentagon_hom_hom_inv_hom_hom · cited by 1Bicategory.pentagon_hom_h…CategoryTheory.Bicategory.pentagon_hom_hom_inv_inv_hom · cited by 1Bicategory.pentagon_hom_h…CategoryTheory.PrelaxFunctor.map₂_iso_inv · cited by 1PrelaxFunctor.map₂_iso_invCategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_inv · cited by 1Bicategory.pentagon_inv_h…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.inv · cited by 467CategoryTheory.invCategoryTheory.Iso.inv_hom_id · cited by 308Iso.inv_hom_idCategoryTheory.IsIso.inv_eq_of_inv_hom_id · cited by 3IsIso.inv_eq_of_inv_hom_idIso.inv_homCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by18

Results whose statement or proof uses this declaration.