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Theorems · Theorem · category theory

CategoryTheory.IsIso.Iso.inv_inv

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ≅ Y), CategoryTheory.inv f.inv = f.hom
Defined in
Mathlib.CategoryTheory.Iso
Cited by
30 results in Mathlib
Foundations
Depth 17 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…AlgebraicGeometry.SpecMap_ΓSpecIso_hom · cited by 8AlgebraicGeometry.SpecMap…CategoryTheory.MonoidalCategory.leftUnitor_inv_whiskerRight · cited by 7MonoidalCategory.leftUnit…CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv · cited by 7Bicategory.whiskerLeft_ri…AlgebraicGeometry.Scheme.toSpecΓ_appTop · cited by 7Scheme.toSpecΓ_appTopAlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app · cited by 5IdealSheafData.subschemeι…CategoryTheory.MonoidalCategory.pentagon_inv · cited by 4MonoidalCategory.pentagon…CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom · cited by 3StrongTrans.naturality_id…CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom · cited by 3StrongTrans.naturality_na…CategoryTheory.Bicategory.leftUnitor_inv_whiskerRight · cited by 3Bicategory.leftUnitor_inv…CategoryTheory.Bicategory.pentagon_inv · cited by 3Bicategory.pentagon_invCategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_hom · cited by 3StrongTrans.naturality_co…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.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_hom_inv_id · cited by 24IsIso.inv_eq_of_hom_inv_idIso.inv_invCITED BYCITES

Cites9

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

Cited by30

Results whose statement or proof uses this declaration.