Theorems · Theorem · category theory

CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.Hom.ext

∀ {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} {x y : D₁.Hom D₂},
  x.hom = y.hom → x = y

Defined in: Mathlib.CategoryTheory.Sites.Descent.DescentDataAsCoalgebra
Cited by: 2 results in Mathlib
Foundations: Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites26

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Functor.mapproof · cited by 8,698
Oppositestatement and proof · cited by 8,081
Quiver.Hom.opproof · cited by 1,948
Prefunctor.objstatement · cited by 1,241
CategoryTheory.PrelaxFunctor.toPrelaxFunctorStructstatement and proof · cited by 1,154
CategoryTheory.PrelaxFunctorStruct.toPrefunctorstatement and proof · cited by 1,142
Prefunctor.mapproof · cited by 952
CategoryTheory.Catstatement and proof · cited by 884
CategoryTheory.Bundled.αstatement · cited by 736

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.hom_extproof · cited by 1
CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.Hom.ext_iffproof · cited by 0