Theorems · Theorem · category theory

CategoryTheory.Subobject.factorThru_arrow_assoc

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (P : CategoryTheory.Subobject Y) (f : X ⟶ Y)
  (h : P.Factors f) {Z : C} (h_1 : Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp (P.factorThru f h) (CategoryTheory.CategoryStruct.comp P.arrow h_1) =
    CategoryTheory.CategoryStruct.comp f h_1

Defined in

Mathlib.CategoryTheory.Subobject.FactorThru

Cited by

3 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category