Theorems · Theorem · category theory

CategoryTheory.comp_rightAdjointMate

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C] {X Y Z : C}
  [inst_2 : CategoryTheory.HasRightDual X] [inst_3 : CategoryTheory.HasRightDual Y]
  [inst_4 : CategoryTheory.HasRightDual Z] {f : X ⟶ Y} {g : Y ⟶ Z},
  CategoryTheory.CategoryStruct.comp f gᘁ = CategoryTheory.CategoryStruct.comp (gᘁ) (fᘁ)

The composition of right adjoint mates is the adjoint mate of the composition.

Defined in

Mathlib.CategoryTheory.Monoidal.Rigid.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.HasRightDualCategoryTheory.HasRightDualCategoryTheory.HasRightDual