Theorems · Theorem · category theory

CategoryTheory.Limits.MonoFactorisation.fac_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} {f : X ⟶ Y}
  (self : CategoryTheory.Limits.MonoFactorisation f) {Z : C} (h : Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp self.e (CategoryTheory.CategoryStruct.comp self.m h) =
    CategoryTheory.CategoryStruct.comp f h

A factorisation of a morphism f = e ≫ m, with m monic.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Images

Cited by

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Foundations

Depth 6 from the axioms · uses Quot.sound

Assumes

CategoryTheory.Category