Theorems · Definition · category theory

CategoryTheory.MorphismProperty.FunctorialFactorizationData.i

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

the first morphism in the factorizations

Defined in: Mathlib.CategoryTheory.MorphismProperty.Factorization
Cited by: 7 results in Mathlib
Foundations: Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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

Cites8

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 · cited by 32,603
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.Arrowstatement · cited by 713
CategoryTheory.Arrow.leftFuncstatement · cited by 37
CategoryTheory.MorphismProperty.FunctorialFactorizationDatastatement and proof · cited by 20
CategoryTheory.MorphismProperty.FunctorialFactorizationData.Zstatement · cited by 10

Cited by10

Results whose statement or proof uses this declaration.

CategoryTheory.MorphismProperty.FunctorialFactorizationData.factorizationDataproof · cited by 10
CategoryTheory.MorphismProperty.FunctorialFactorizationData.facstatement · cited by 2
CategoryTheory.MorphismProperty.FunctorialFactorizationData.i_mapZproof · cited by 1
CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_appstatement and proof · cited by 1
CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app_assocstatement and proof · cited by 0
CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_assocstatement and proof · cited by 0
CategoryTheory.MorphismProperty.FunctorialFactorizationData.histatement · cited by 0
CategoryTheory.MorphismProperty.FunctorialFactorizationData.ofLEproof · cited by 0
CategoryTheory.SmallObject.functorialFactorizationData_i_appstatement and proof · cited by 0
CategoryTheory.Sheaf.functorialLocallySurjectiveInjectiveFactorizationproof · cited by 0