Theorems · Definition · category theory

CategoryTheory.tensorRightHomEquiv

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      (X Y Y' Z : C) →
        [CategoryTheory.ExactPairing Y Y'] →
          (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y ⟶ Z) ≃
            (X ⟶ CategoryTheory.MonoidalCategoryStruct.tensorObj Z Y')

Given an exact pairing on Y Y', we get a bijection on hom-sets (X ⊗ Y ⟶ Z) ≃ (X ⟶ Z ⊗ Y') by "pulling the string on the right" up or down.

Defined in

Mathlib.CategoryTheory.Monoidal.Rigid.Basic

Cited by

9 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.ExactPairing