Theorems · Theorem · category theory
CategoryTheory.IsIso.of_isIso_comp_left
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z) [CategoryTheory.IsIso f]
[CategoryTheory.IsIso (CategoryTheory.CategoryStruct.comp f g)], CategoryTheory.IsIso g- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, 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 and proof · 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.invproof · cited by 467
- CategoryTheory.IsIso.inv_hom_idproof · cited by 88
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.RightHomologyMapData.quasiIso_iffproof · cited by 6
- CategoryTheory.ShortComplex.LeftHomologyMapData.quasiIso_iffproof · cited by 6
- CategoryTheory.isIso_comp_left_iffproof · cited by 4
- CategoryTheory.Functor.final_of_final_compproof · cited by 4
- CategoryTheory.IsIso.of_isIso_fac_leftproof · cited by 2
- CategoryTheory.ShortComplex.quasiIso_of_comp_leftproof · cited by 1
- CochainComplex.mappingCone.quasiIso_descShortComplexproof · cited by 1
- quasiIsoAt_of_comp_leftproof · cited by 1