Theorems · Definition · category theory

CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.obj

{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} → F.DescentDataAsCoalgebra f → (i : ι) → ↑(F.obj { as := Opposite.op (X i) }).obj

The objects over X i for all i

Defined in: Mathlib.CategoryTheory.Sites.Descent.DescentDataAsCoalgebra
Cited by: 29 results in Mathlib
Foundations: Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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

Cites14

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
Oppositestatement and proof · cited by 8,081
Prefunctor.objstatement · cited by 1,241
CategoryTheory.PrelaxFunctor.toPrelaxFunctorStructstatement · cited by 1,154
CategoryTheory.PrelaxFunctorStruct.toPrefunctorstatement · cited by 1,142
CategoryTheory.Catstatement and proof · cited by 884
CategoryTheory.Bundled.αstatement · cited by 736
CategoryTheory.Pseudofunctor.toPrelaxFunctorstatement · cited by 640
CategoryTheory.Pseudofunctorstatement and proof · cited by 571
CategoryTheory.LocallyDiscretestatement and proof · cited by 318
CategoryTheory.Bicategory.Adjstatement and proof · cited by 131

Cited by38

Results whose statement or proof uses this declaration.

CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.homstatement · cited by 22
CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.Hom.homstatement · cited by 18
CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalenceproof · cited by 13
CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.isoMkstatement and proof · cited by 3
CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.Hom.extstatement and proof · cited by 2
CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.Hom.commstatement · cited by 1
CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coassocstatement · cited by 1
CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.comp_homstatement · cited by 1
CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.counitstatement · cited by 1
CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.hom_extstatement · cited by 1
CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.Hom.mk.injstatement and proof · cited by 1
CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.Hom.mk.noConfusionstatement and proof · cited by 1