Theorems · Theorem · category theory

CategoryTheory.Adjunction.Triple.whiskerRight_rightToLeft_assoc

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C}
  {H : CategoryTheory.Functor C D} (t : CategoryTheory.Adjunction.Triple F G H) [inst_2 : G.Full] [inst_3 : G.Faithful]
  {Z : CategoryTheory.Functor C C} (h : F.comp G ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.whiskerRight t.rightToLeft G) h =
    CategoryTheory.CategoryStruct.comp t.adj₂.counit (CategoryTheory.CategoryStruct.comp t.adj₁.unit h)

For an adjoint triple F ⊣ G ⊣ H where G is fully faithful, whiskering the natural transformation H ⟶ F with G yields the composition of the counit of the second adjunction with the unit of the first adjunction.

Defined in

Mathlib.CategoryTheory.Adjunction.Triple

Cited by

0 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FullCategoryTheory.Functor.Faithful