Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.ProEt.equivOfIsEmpty
(S : AlgebraicGeometry.Scheme) → [IsEmpty ↥S] → S.ProEt ≌ CategoryTheory.Discrete PUnit.{u_1 + 1}If S is the empty scheme, the pro-étale site over S is a point.
- Defined in
- Mathlib.AlgebraicGeometry.Sites.Proetale
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsEmpty
Around this declaration
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
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- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
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- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- IsEmptystatement and proof · cited by 759
- CategoryTheory.Equivalencestatement · cited by 601
- AlgebraicGeometry.WeaklyEtaleproof · cited by 14
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