Theorems · Definition · category theory
CategoryTheory.Functor.PreOneHypercoverDenseData.f
{C₀ : Type u₀} →
{C : Type u} →
[inst : CategoryTheory.Category.{v₀, u₀} C₀] →
[inst_1 : CategoryTheory.Category.{v, u} C] →
{F : CategoryTheory.Functor C₀ C} →
{S : C} → (self : F.PreOneHypercoverDenseData S) → (i : self.I₀) → F.obj (self.X i) ⟶ Sthe morphisms in the covering of S
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.PreOneHypercoverDenseData.I₀statement · cited by 45
- CategoryTheory.Functor.PreOneHypercoverDenseData.Xstatement · cited by 44
- CategoryTheory.Functor.PreOneHypercoverDenseDatastatement and proof · cited by 27
Cited by46
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.PreOneHypercoverDenseData.toPreOneHypercoverproof · cited by 17
- CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMapproof · cited by 13
- CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_πstatement and proof · cited by 5
- CategoryTheory.Functor.OneHypercoverDenseData.SieveStruct.facstatement · cited by 3
- CategoryTheory.Functor.OneHypercoverDenseData.mem₁₀statement · cited by 3
- CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObj_mapPreimage_conditionstatement and proof · cited by 3
- CategoryTheory.Functor.OneHypercoverDenseData.essSurj.restriction_mapstatement and proof · cited by 3
- CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso.inv_πstatement and proof · cited by 3
- CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafMap_presheafObjObjIso_homstatement and proof · cited by 2
- CategoryTheory.Functor.OneHypercoverDenseData.essSurj.restriction_eq_of_facstatement and proof · cited by 2