Theorems · Theorem · category theory
CategoryTheory.isIso_comp_left_iff
∀ {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
- 4 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.IsIsostatement and proof · cited by 1,156
- CategoryTheory.IsIso.of_isIso_comp_leftproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isIso_pushoutSection_of_isQuasiSeparated_of_flat_leftproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.isIso_iff_finrank_eqproof · cited by 0
- AlgebraicGeometry.isIso_fromTildeΓ_iff_isLocalizingproof · cited by 0