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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
Assumes
CategoryTheory.CategoryCategoryTheory.IsIso

Around this declaration

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

CategoryTheory.IsIso.inv_comp · cited by 22IsIso.inv_compAlgebraicGeometry.Scheme.Cover.ι_glueMorphisms · cited by 12Cover.ι_glueMorphismsCategoryTheory.MorphismProperty.RightFraction.map_s_comp_map · cited by 5RightFraction.map_s_comp_…DerivedCategory.right_fac_of_isStrictlyLE · cited by 3DerivedCategory.right_fac…CategoryTheory.ObjectProperty.SerreClassLocalization.preservesCokernel · cited by 3SerreClassLocalization.pr…CategoryTheory.ObjectProperty.isLocal_of_isIso · cited by 2ObjectProperty.isLocal_of…CochainComplex.IsKInjective.quasiIso_iff · cited by 2IsKInjective.quasiIso_iffDerivedCategory.descShortComplex_triangleOfSESδ · cited by 2DerivedCategory.descShort…CategoryTheory.IsPushout.of_horiz_isIso_epi · cited by 2IsPushout.of_horiz_isIso_…AlgebraicGeometry.isIso_pushoutSection_of_iSup_eq · cited by 2AlgebraicGeometry.isIso_p…CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_fac · cited by 2TStructure.eTruncLTGEIsoG…CategoryTheory.Triangulated.TStructure.isIso_truncGE_map_iff · cited by 2TStructure.isIso_truncGE_…CategoryTheory.Adjunction.hasLeftCalculusOfFractions · cited by 2Adjunction.hasLeftCalculu…CategoryTheory.Groupoid.isThin_iff · cited by 1Groupoid.isThin_iffCategoryTheory.Limits.BinaryCofan.isColimit_iff_isIso_inl · cited by 1BinaryCofan.isColimit_iff…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.Category.id_comp · cited by 1998Category.id_compCategoryTheory.IsIso · cited by 1156CategoryTheory.IsIsoCategoryTheory.inv · cited by 467CategoryTheory.invCategoryTheory.IsIso.hom_inv_id · cited by 97IsIso.hom_inv_idIsIso.hom_inv_id_assocCITED BYCITES

Cites8

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

Cited by29

Results whose statement or proof uses this declaration.