Theorems · Theorem · category theory

CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.Hom.comm

∀ {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} {D₁ D₂ : F.DescentDataAsCoalgebra f} (self : D₁.Hom D₂)
  (i₁ i₂ : ι),
  CategoryTheory.CategoryStruct.comp (D₁.hom i₁ i₂)
      ((F.map (f i₁).op.toLoc).l.toFunctor.map ((F.map (f i₂).op.toLoc).r.toFunctor.map (self.hom i₂))) =
    CategoryTheory.CategoryStruct.comp (self.hom i₁) (D₂.hom i₁ i₂)

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