Theorems · Theorem · category theory
CategoryTheory.Iso.inv_comp_eq
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} (α : X ≅ Y) {f : X ⟶ Z} {g : Y ⟶ Z},
CategoryTheory.CategoryStruct.comp α.inv f = g ↔ f = CategoryTheory.CategoryStruct.comp α.hom g- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
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 and proof · cited by 17,999
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.Iso.invstatement and proof · cited by 6,514
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.Iso.inv_hom_id_assocproof · cited by 275
- CategoryTheory.Iso.hom_inv_id_assocproof · cited by 187
Cited by50
Results whose statement or proof uses this declaration.
- CategoryTheory.Iso.eq_inv_compproof · cited by 34
- CategoryTheory.IsIso.inv_comp_eqproof · cited by 12
- CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_π_appproof · cited by 6
- CategoryTheory.Subobject.eq_of_commproof · cited by 5
- CategoryTheory.Limits.pullbackAssoc_inv_sndproof · cited by 4
- CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_fstproof · cited by 4
- CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_sndproof · cited by 4
- AlgebraicGeometry.AffineSpace.SpecIso_inv_overproof · cited by 4
- CompHaus.effectiveEpiFamily_tfaeproof · cited by 3
- CategoryTheory.Limits.pullbackAssoc_inv_fst_sndproof · cited by 3
- AlgebraicGeometry.Proj.awayι_comp_mapproof · cited by 3
- AlgebraicGeometry.IsAffineOpen.fromSpec_topproof · cited by 3