Theorems · Theorem · category theory

CategoryTheory.Adjunction.Triple.whiskerLeft_leftToRight

∀ {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 : F.Full] [inst_3 : F.Faithful],
  G.whiskerLeft t.leftToRight = CategoryTheory.CategoryStruct.comp t.adj₁.counit t.adj₂.unit

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

Defined in

Mathlib.CategoryTheory.Adjunction.Triple

Cited by

1 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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