Theorems · Definition · category theory

CategoryTheory.MorphismProperty.FunctorialFactorizationData.Z

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {W₁ W₂ : CategoryTheory.MorphismProperty C} →
      W₁.FunctorialFactorizationData W₂ → CategoryTheory.Functor (CategoryTheory.Arrow C) C

the intermediate objects in the factorizations

Defined in: Mathlib.CategoryTheory.MorphismProperty.Factorization
Cited by: 10 results in Mathlib
Foundations: Depth 17 from the axioms · uses propext, Quot.sound
Assumes: CategoryTheory.Category

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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
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.Arrowstatement · cited by 713
CategoryTheory.MorphismProperty.FunctorialFactorizationDatastatement and proof · cited by 20

Cited by16

Results whose statement or proof uses this declaration.

CategoryTheory.MorphismProperty.FunctorialFactorizationData.factorizationDataproof · cited by 10
CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZproof · cited by 9
CategoryTheory.MorphismProperty.FunctorialFactorizationData.istatement · cited by 7
CategoryTheory.MorphismProperty.FunctorialFactorizationData.pstatement · cited by 7
CategoryTheory.MorphismProperty.FunctorialFactorizationData.facstatement · cited by 2
CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_compproof · cited by 1
CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_appstatement · cited by 1
CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app_assocstatement · cited by 0
CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_assocstatement · cited by 0
CategoryTheory.MorphismProperty.FunctorialFactorizationData.histatement · cited by 0
CategoryTheory.MorphismProperty.FunctorialFactorizationData.hpstatement · cited by 0
CategoryTheory.MorphismProperty.FunctorialFactorizationData.mapZ_idproof · cited by 0