Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.of_isIso
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.MorphismProperty C) [P.ContainsIdentities]
[P.RespectsIso] {X Y : C} (f : X ⟶ Y) [CategoryTheory.IsIso f], P f- Cited by
- 5 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.idproof · cited by 6,235
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.MorphismProperty.RespectsIsostatement and proof · cited by 248
- CategoryTheory.MorphismProperty.ContainsIdentitiesstatement and proof · cited by 94
- CategoryTheory.MorphismProperty.id_memproof · cited by 23
- CategoryTheory.MorphismProperty.RespectsIso.postcompproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.coverOfIsIsoproof · cited by 9
- SSet.innerAnodyneExtensions.of_isIsoproof · cited by 1
- SSet.anodyneExtensions.of_isIsoproof · cited by 1
- CategoryTheory.MorphismProperty.isomorphisms_le_of_containsIdentitiesproof · cited by 0