Theorems · Theorem · category theory

CategoryTheory.Adjunction.inv_counit_map

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {L : CategoryTheory.Functor C D} {R : CategoryTheory.Functor D C} (h : L ⊣ R) {X : D}
  [inst_2 : CategoryTheory.IsIso (h.counit.app X)], CategoryTheory.inv (R.map (h.counit.app X)) = h.unit.app (R.obj X)

If the counit of an adjunction is an isomorphism, then its inverse on the image of R is given by R whiskered with the unit.

Defined in

Mathlib.CategoryTheory.Adjunction.FullyFaithful

Cited by

4 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.IsIso