Theorems · Definition · category theory
CategoryTheory.MorphismProperty.MapFactorizationData.opEquiv
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
{W₁ W₂ : CategoryTheory.MorphismProperty C} →
{X Y : C} → {f : X ⟶ Y} → W₁.MapFactorizationData W₂ f ≃ W₂.op.MapFactorizationData W₁.op f.opThe bijection between factorizations in C and factorizations in Cᵒᵖ.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- CategoryTheory.Category
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
- Equivstatement · cited by 8,337
- Oppositestatement · cited by 8,081
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- Quiver.Hom.opstatement and proof · cited by 1,948
- CategoryTheory.MorphismProperty.opstatement and proof · cited by 71
- CategoryTheory.MorphismProperty.MapFactorizationDatastatement and proof · cited by 63
- CategoryTheory.MorphismProperty.MapFactorizationData.opproof · cited by 4
- CategoryTheory.MorphismProperty.MapFactorizationData.unopproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.MapFactorizationData.opEquiv_applystatement and proof · cited by 0
- CategoryTheory.MorphismProperty.MapFactorizationData.opEquiv_symm_applystatement and proof · cited by 0