Theorems · Definition · category theory

CategoryTheory.tensorClosed

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      {X Y : C} →
        CategoryTheory.Closed X →
          CategoryTheory.Closed Y → CategoryTheory.Closed (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y)

If X and Y are closed then X ⊗ Y is. This isn't an instance because it's not usually how we want to construct internal homs, we'll usually prove all objects are closed uniformly.

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.Basic

Cited by

0 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategory