Theorems · Theorem · category theory

CategoryTheory.Under.postAdjunctionRight_unit_app_right

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  [inst_2 : CategoryTheory.Limits.HasPushouts D] {Y : D} {F : CategoryTheory.Functor C D}
  {G : CategoryTheory.Functor D C} (a : F ⊣ G) (X : CategoryTheory.Under ((CategoryTheory.Functor.id C).obj (G.1 Y))),
  ((CategoryTheory.Under.postAdjunctionRight a).unit.app X).right =
    CategoryTheory.CategoryStruct.comp (a.unit.app X.right)
      (G.map (CategoryTheory.Limits.pushout.inl (F.map X.hom) (a.counit.app Y)))

Defined in

Mathlib.CategoryTheory.Comma.Over.Pullback

Cited by

0 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasPushouts