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Theorems · Theorem · category theory

CategoryTheory.IsIso.inv_hom_id_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y) [I : CategoryTheory.IsIso f] {Z : C}
  (h : Y ⟶ Z), CategoryTheory.CategoryStruct.comp (CategoryTheory.inv f) (CategoryTheory.CategoryStruct.comp f h) = h
Defined in
Mathlib.CategoryTheory.Iso
Cited by
37 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.MorphismProperty.cancel_left_of_respectsIso · cited by 33MorphismProperty.cancel_l…RingHom.RespectsIso.cancel_left_isIso · cited by 6RespectsIso.cancel_left_i…CategoryTheory.GlueData.t_inv · cited by 6GlueData.t_invAlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_invApp · cited by 5IsOpenImmersion.inv_invAppAlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality · cited by 5IsOpenImmersion.inv_natur…CategoryTheory.IsVanKampenColimit.precompose_isIso_iff · cited by 4IsVanKampenColimit.precom…AlgebraicGeometry.IsClosedImmersion.lift_fac · cited by 4IsClosedImmersion.lift_facCategoryTheory.IsPullback.of_horiz_isIso_mono · cited by 4IsPullback.of_horiz_isIso…AlgebraicGeometry.Scheme.Hom.ker_comp_of_isIso · cited by 4Hom.ker_comp_of_isIsoAlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.lift_fac · cited by 3IsOpenImmersion.lift_facCategoryTheory.ObjectProperty.SerreClassLocalization.preservesKernel · cited by 3SerreClassLocalization.pr…CategoryTheory.Pretriangulated.isIso₂_of_isIso₁₃ · cited by 3Pretriangulated.isIso₂_of…CategoryTheory.IsVanKampenColimit.map_reflective · cited by 2IsVanKampenColimit.map_re…AlgebraicGeometry.isIso_pushoutSection_of_iSup_eq · cited by 2AlgebraicGeometry.isIso_p…DerivedCategory.left_fac_of_isStrictlyGE · cited by 2DerivedCategory.left_fac_…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.inv_hom_id · cited by 88IsIso.inv_hom_idIsIso.inv_hom_id_assocCITED BYCITES

Cites8

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

Cited by37

Results whose statement or proof uses this declaration.