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Theorems · Definition · category theory

CategoryTheory.MorphismProperty.MapFactorizationData.Z

{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 → C

the intermediate object in the factorization

Defined in
Mathlib.CategoryTheory.MorphismProperty.Factorization
Cited by
63 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.Category
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.MorphismProperty.MapFactorizationData.i · cited by 36MapFactorizationData.iCategoryTheory.MorphismProperty.MapFactorizationData.p · cited by 36MapFactorizationData.pHomotopicalAlgebra.ReedyStructure.degHom · cited by 13ReedyStructure.degHomCategoryTheory.MorphismProperty.MapFactorizationData.fac · cited by 9MapFactorizationData.facCategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ · cited by 9FunctorialFactorizationDa…CategoryTheory.MorphismProperty.MapFactorizationData.hi · cited by 7MapFactorizationData.hiCategoryTheory.MorphismProperty.MapFactorizationData.hp · cited by 7MapFactorizationData.hpHomotopicalAlgebra.PathObject.ofFactorizationData · cited by 6PathObject.ofFactorizatio…HomotopicalAlgebra.Cylinder.ofFactorizationData · cited by 6Cylinder.ofFactorizationD…HomotopicalAlgebra.ReedyStructure.exists_fac · cited by 5ReedyStructure.exists_facCategoryTheory.MorphismProperty.MapFactorizationData.fac_assoc · cited by 5MapFactorizationData.fac_…HomotopicalAlgebra.FibrantBrownFactorization.mk' · cited by 4FibrantBrownFactorization…HomotopicalAlgebra.FibrantBrownFactorization.r · cited by 4FibrantBrownFactorization…HomotopicalAlgebra.CofibrantBrownFactorization.mk' · cited by 4CofibrantBrownFactorizati…HomotopicalAlgebra.CofibrantBrownFactorization.s · cited by 4CofibrantBrownFactorizati…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.MorphismProperty.MapFactorizationData · cited by 63MorphismProperty.MapFacto…MapFactorizationData.ZCITED BYCITES

Cites4

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Cited by87

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