Theorems · Theorem · category theory

CategoryTheory.Limits.MonoFactorisation.fac_apply

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {F G : CategoryTheory.Functor C (Type w)} {f : F ⟶ G} {X : C}
  (H : CategoryTheory.Limits.MonoFactorisation f) (x : F.obj X),
  (CategoryTheory.ConcreteCategory.hom (H.m.app X)) ((CategoryTheory.ConcreteCategory.hom (H.e.app X)) x) =
    (CategoryTheory.ConcreteCategory.hom (f.app X)) x

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Images

Cited by

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Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category