Theorems · Theorem · category theory

CategoryTheory.prod_comp

∀ {C : Type u₁} [inst : CategoryTheory.CategoryStruct.{v₁, u₁} C] {D : Type u₂}
  [inst_1 : CategoryTheory.CategoryStruct.{v₂, u₂} D] {P Q R : C} {S T U : D} (f : (P, S) ⟶ (Q, T))
  (g : (Q, T) ⟶ (R, U)),
  CategoryTheory.CategoryStruct.comp f g =
    CategoryTheory.Prod.mkHom (CategoryTheory.CategoryStruct.comp f.1 g.1) (CategoryTheory.CategoryStruct.comp f.2 g.2)

Defined in

Mathlib.CategoryTheory.Products.Basic

Cited by

5 results in Mathlib

Foundations

Depth 5 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryStructCategoryTheory.CategoryStruct