Theorems · Definition · category theory

CategoryTheory.Over.postAdjunctionRight

{T : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} T] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {Y : D} →
          {F : CategoryTheory.Functor T D} →
            {G : CategoryTheory.Functor D T} →
              (a : F ⊣ G) →
                (CategoryTheory.Over.post F).comp (CategoryTheory.Over.map (a.counit.app Y)) ⊣
                  CategoryTheory.Over.post G

If G is a right adjoint, then so is post G : Over Y ⥤ Over (G Y). If the left adjoint of G is F, then the left adjoint of post G is given by (X ⟶ G Y) ↦ (F X ⟶ F G Y ⟶ Y).

Defined in

Mathlib.CategoryTheory.Comma.Over.Basic

Cited by

4 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category