Theorems · Theorem · category theory

CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.counit_assoc

∀ {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)
  {Z : ↑(F.obj { as := Opposite.op (X i) }).obj}
  (h : (CategoryTheory.CategoryStruct.id (F.obj { as := Opposite.op (X i) }).obj).toFunctor.obj (self.obj i) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (self.hom i i)
      (CategoryTheory.CategoryStruct.comp ((F.map (f i).op.toLoc).adj.counit.toNatTrans.app (self.obj i)) h) =
    h

Defined in

Mathlib.CategoryTheory.Sites.Descent.DescentDataAsCoalgebra

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.Category