Theorems · Theorem · category theory
CategoryTheory.IsIso.hom_inv_id_assoc
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y) [I : CategoryTheory.IsIso f] {Z : C}
(h : X ⟶ Z), CategoryTheory.CategoryStruct.comp f (CategoryTheory.CategoryStruct.comp (CategoryTheory.inv f) h) = h- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.invstatement and proof · cited by 467
- CategoryTheory.IsIso.hom_inv_idproof · cited by 97
Cited by29
Results whose statement or proof uses this declaration.
- CategoryTheory.IsIso.inv_compproof · cited by 22
- AlgebraicGeometry.Scheme.Cover.ι_glueMorphismsproof · cited by 12
- CategoryTheory.MorphismProperty.RightFraction.map_s_comp_mapproof · cited by 5
- DerivedCategory.right_fac_of_isStrictlyLEproof · cited by 3
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesCokernelproof · cited by 3
- CategoryTheory.ObjectProperty.isLocal_of_isIsoproof · cited by 2
- CochainComplex.IsKInjective.quasiIso_iffproof · cited by 2
- DerivedCategory.descShortComplex_triangleOfSESδproof · cited by 2
- CategoryTheory.IsPushout.of_horiz_isIso_epiproof · cited by 2
- AlgebraicGeometry.isIso_pushoutSection_of_iSup_eqproof · cited by 2
- CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_facproof · cited by 2
- CategoryTheory.Triangulated.TStructure.isIso_truncGE_map_iffproof · cited by 2