Theorems · Definition · category theory

CategoryTheory.MonoidalClosed.compTranspose

{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
                (CategoryTheory.MonoidalCategoryStruct.tensorObj (x ⟹ y) (y ⟹ z)) ⟶
              z

The uncurried composition morphism x ⊗ (hom(x, y) ⊗ hom(y, z)) ⟶ (x ⊗ hom(x, y)) ⊗ hom(y, z) ⟶ y ⊗ hom(y, z) ⟶ z. The C-composition morphism will be defined as the adjoint transpose of this map.

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.Basic

Cited by

7 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.ClosedCategoryTheory.Closed