Theorems · Theorem · category theory

CategoryTheory.Pseudofunctor.isEquivalence_toDescentDataAsCoalgebra_iff_isEquivalence_comonadComparison

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C]
  {F :
    CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete Cᵒᵖ)
      (CategoryTheory.Bicategory.Adj CategoryTheory.Cat)}
  (ι : Type u_1) [Unique ι] {X S : C} (f : X ⟶ S),
  (F.toDescentDataAsCoalgebra fun x => f).IsEquivalence ↔
    (CategoryTheory.Comonad.comparison (CategoryTheory.Adjunction.ofCat (F.map f.op.toLoc).adj)).IsEquivalence

Defined in

Mathlib.CategoryTheory.Sites.Descent.DescentDataAsCoalgebra

Cited by

0 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryUnique