Theorems · Definition · category theory
TopCat.Presheaf.presieveOfCoveringAux
{X : TopCat} →
{ι : Type v} → (ι → TopologicalSpace.Opens ↑X) → (Y : TopologicalSpace.Opens ↑X) → CategoryTheory.Presieve YGiven a family of opens U : ι → Opens X and any open Y : Opens X, we obtain a presieve
on Y by declaring that a morphism f : V ⟶ Y is a member of the presieve if and only if
there exists an index i : ι such that V = U i.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- TopCat.carrierstatement and proof · cited by 3,184
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- TopCatstatement and proof · cited by 1,889
- CategoryTheory.Presievestatement · cited by 449
Cited by20
Results whose statement or proof uses this declaration.
- TopCat.Presheaf.generateEquivalenceOpensLe_inverse'statement · cited by 7
- TopCat.Presheaf.generateEquivalenceOpensLestatement · cited by 6
- TopCat.Presheaf.generateEquivalenceOpensLe_functor'statement and proof · cited by 5
- TopCat.Presheaf.presieveOfCoveringproof · cited by 2
- TopCat.Presheaf.IsSheaf.isSheafOpensLeCoverproof · cited by 2
- TopCat.Presheaf.whiskerIsoMapGenerateCoconestatement and proof · cited by 2
- TopCat.Presheaf.isLimitOpensLeEquivGenerate₁statement · cited by 1
- TopCat.Presheaf.covering_presieve_eq_selfstatement and proof · cited by 0
- TopCat.Presheaf.generateEquivalenceOpensLe_counitIsostatement · cited by 0
- TopCat.Presheaf.generateEquivalenceOpensLe_functorstatement · cited by 0
- TopCat.Presheaf.generateEquivalenceOpensLe_functor'_mapstatement and proof · cited by 0
- TopCat.Presheaf.generateEquivalenceOpensLe_functor'_obj_objstatement and proof · cited by 0