Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {W₁ W₂ : CategoryTheory.MorphismProperty C}
  (data : W₁.FunctorialFactorizationData W₂) {f : CategoryTheory.Arrow C},
  CategoryTheory.CategoryStruct.comp (data.i.app f) (data.p.app f) = f.hom

Defined in: Mathlib.CategoryTheory.MorphismProperty.Factorization
Cited by: 1 results in Mathlib
Foundations: Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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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.Functor.objstatement and proof · cited by 19,642
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.Arrowstatement and proof · cited by 713
CategoryTheory.Arrow.leftproof · cited by 426
CategoryTheory.Arrow.rightproof · cited by 423
CategoryTheory.Arrow.homstatement and proof · cited by 335
CategoryTheory.Arrow.leftFuncstatement and proof · cited by 37
CategoryTheory.Arrow.rightFuncstatement and proof · cited by 32

Cited by1

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CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app_assocproof · cited by 0