Theorems · Theorem · category theory

CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_left

∀ {C₁ : Type u₁} {C₂ : Type u₂} {C₃ : Type u₃} [inst : CategoryTheory.Category.{v₁, u₁} C₁]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] [inst_2 : CategoryTheory.Category.{v₃, u₃} C₃]
  (F : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ C₃))
  (G : CategoryTheory.Functor C₁ᵒᵖ (CategoryTheory.Functor C₃ C₂)) (adj₂ : F ⊣₂ G) (X₁ : CategoryTheory.Arrow C₁)
  [inst_3 : CategoryTheory.Limits.HasPullbacks C₂] [inst_4 : CategoryTheory.Limits.HasPushouts C₃]
  (X₂ : CategoryTheory.Arrow C₂),
  ((CategoryTheory.Functor.LeibnizAdjunction.adj F G adj₂ X₁).unit.app X₂).left =
    adj₂.homEquiv (CategoryTheory.Limits.pushout.inl ((F.map X₁.hom).app X₂.left) ((F.obj X₁.left).map X₂.hom))

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj

Cited by

0 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksCategoryTheory.Limits.HasPushouts