Theorems · Theorem · category theory

CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.counit

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C]
  {F :
    CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete Cᵒᵖ)
      (CategoryTheory.Bicategory.Adj CategoryTheory.Cat)}
  {ι : Type t} {S : C} {X : ι → C} {f : (i : ι) → X i ⟶ S} (self : F.DescentDataAsCoalgebra f) (i : ι),
  CategoryTheory.CategoryStruct.comp (self.hom i i) ((F.map (f i).op.toLoc).adj.counit.toNatTrans.app (self.obj i)) =
    CategoryTheory.CategoryStruct.id (self.obj i)

Defined in

Mathlib.CategoryTheory.Sites.Descent.DescentDataAsCoalgebra

Cited by

1 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category