Theorems · Definition · category theory

CategoryTheory.MonoidalClosed.comp

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      (x y z : C) →
        [inst_2 : CategoryTheory.Closed x] →
          [inst_3 : CategoryTheory.Closed y] → CategoryTheory.MonoidalCategoryStruct.tensorObj (x ⟹ y) (y ⟹ z) ⟶ x ⟹ z

The C-composition morphism hom(x, y) ⊗ hom(y, z) ⟶ hom(x, z) used to equip C with the structure of a C-category

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.Basic

Cited by

13 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.ClosedCategoryTheory.Closed