Theorems · Definition · category theory
CategoryTheory.MorphismProperty.MapFactorizationData.i
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
{W₁ W₂ : CategoryTheory.MorphismProperty C} →
{X Y : C} → {f : X ⟶ Y} → (self : W₁.MapFactorizationData W₂ f) → X ⟶ self.Zthe first morphism in the factorization
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
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.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.MorphismProperty.MapFactorizationDatastatement and proof · cited by 63
- CategoryTheory.MorphismProperty.MapFactorizationData.Zstatement · cited by 63
Cited by49
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.MapFactorizationData.facstatement · cited by 9
- CategoryTheory.MorphismProperty.MapFactorizationData.histatement · cited by 7
- HomotopicalAlgebra.PathObject.ofFactorizationDataproof · cited by 6
- HomotopicalAlgebra.Cylinder.ofFactorizationDataproof · cited by 6
- HomotopicalAlgebra.ReedyStructure.exists_facproof · cited by 5
- CategoryTheory.MorphismProperty.MapFactorizationData.fac_assocstatement and proof · cited by 5
- CategoryTheory.Sheaf.isLocallySurjective_iff_epi'proof · cited by 5
- HomotopicalAlgebra.FibrantBrownFactorization.mk'proof · cited by 4
- HomotopicalAlgebra.CofibrantBrownFactorization.mk'proof · cited by 4
- CategoryTheory.MorphismProperty.MapFactorizationData.opproof · cited by 4
- CategoryTheory.MorphismProperty.MapFactorizationData.unopproof · cited by 4
- HomotopicalAlgebra.RightHomotopyRel.exists_very_good_pathObjectproof · cited by 3