Theorems · Definition · category theory

CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence

{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.DescentDataAsCoalgebra fun x => f) ≌
                (CategoryTheory.Adjunction.ofCat (F.map f.op.toLoc).adj).toComonad.Coalgebra

When the index type ι contains a unique element, the category DescentDataAsCoalgebra identifies to the category of coalgebras over the comonad corresponding to the adjunction (F.map f.op.toLoc).adj.

Defined in

Mathlib.CategoryTheory.Sites.Descent.DescentDataAsCoalgebra

Cited by

13 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryUnique