Theorems · Theorem · category theory

CategoryTheory.EnrichedFunctor.map_comp

∀ {V : Type v} [inst : CategoryTheory.Category.{w, v} V] [inst_1 : CategoryTheory.MonoidalCategory V] {C : Type u₁}
  [inst_2 : CategoryTheory.EnrichedCategory V C] {D : Type u₂} [inst_3 : CategoryTheory.EnrichedCategory V D]
  (self : CategoryTheory.EnrichedFunctor V C D) (X Y Z : C),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.eComp V X Y Z) (self.map X Z) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.tensorHom (self.map X Y) (self.map Y Z))
      (CategoryTheory.eComp V (self.obj X) (self.obj Y) (self.obj Z))

Defined in

Mathlib.CategoryTheory.Enriched.Basic

Cited by

2 results in Mathlib

Foundations

Depth 6 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.EnrichedCategoryCategoryTheory.EnrichedCategory