Theorems · Definition · category theory

CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.hom

{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) →
                (i₁ i₂ : ι) →
                  self.obj i₁ ⟶
                    (F.map (f i₁).op.toLoc).l.toFunctor.obj ((F.map (f i₂).op.toLoc).r.toFunctor.obj (self.obj i₂))

The compatibility morphisms.

Defined in

Mathlib.CategoryTheory.Sites.Descent.DescentDataAsCoalgebra

Cited by

22 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category