Theorems · Definition · category theory

CategoryTheory.Functor.closedCounit

{D : Type u} →
  {C : Type u_1} →
    [inst : CategoryTheory.Groupoid D] →
      [inst_1 : CategoryTheory.Category.{v_1, u_1} C] →
        [inst_2 : CategoryTheory.MonoidalCategory C] →
          [inst_3 : CategoryTheory.MonoidalClosed C] →
            (F : CategoryTheory.Functor D C) →
              F.closedIhom.comp (CategoryTheory.MonoidalCategory.tensorLeft F) ⟶
                CategoryTheory.Functor.id (CategoryTheory.Functor D C)

Auxiliary definition for CategoryTheory.Functor.closed. The counit for the adjunction (tensorLeft F) ⊣ (ihom F).

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Groupoid

Cited by

3 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.GroupoidCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalClosed