Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.ofArrows_mem_smallEtaleTopology_iff
∀ {X : AlgebraicGeometry.Scheme} {W : X.Etale} {ι : Type u_1} {Z : ι → X.Etale} (f : (i : ι) → Z i ⟶ W),
CategoryTheory.Sieve.ofArrows Z f ∈ X.smallEtaleTopology W ↔ ⋃ i, Set.range ⇑(f i).left = Set.univ- Defined in
- Mathlib.AlgebraicGeometry.Sites.Etale
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites65
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Top.topstatement and proof · cited by 9,680
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- Set.rangestatement and proof · cited by 4,705
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- Set.univstatement and proof · cited by 3,945
- CategoryTheory.Functor.idstatement · cited by 3,333
- TopCat.carrierstatement and proof · cited by 3,184
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.isConservative_pointSmallEtaleproof · cited by 1