Theorems · Theorem · category theory

CategoryTheory.OverClass.asOverHom_comp_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} (S : C) [inst_1 : CategoryTheory.OverClass X S]
  [inst_2 : CategoryTheory.OverClass Y S] [inst_3 : CategoryTheory.OverClass Z S] (f : X ⟶ Y) (g : Y ⟶ Z)
  [inst_4 : CategoryTheory.HomIsOver f S] [inst_5 : CategoryTheory.HomIsOver g S] {Z_1 : CategoryTheory.Over S}
  (h : CategoryTheory.OverClass.asOver Z S ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.OverClass.asOverHom S (CategoryTheory.CategoryStruct.comp f g)) h =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.OverClass.asOverHom S f)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.OverClass.asOverHom S g) h)

Defined in

Mathlib.CategoryTheory.Comma.Over.OverClass

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.OverClassCategoryTheory.OverClassCategoryTheory.OverClassCategoryTheory.HomIsOverCategoryTheory.HomIsOver