Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isInitial_iff_isEmpty
∀ {X : AlgebraicGeometry.Scheme}, Nonempty (CategoryTheory.Limits.IsInitial X) ↔ IsEmpty ↥X- Defined in
- Mathlib.AlgebraicGeometry.Limits
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Iso.homproof · cited by 7,684
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- 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.Limits.IsInitialstatement and proof · cited by 158
- Homeomorph.toEquivproof · cited by 77
- AlgebraicGeometry.Scheme.Hom.homeomorphproof · cited by 13
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