Theorems · Definition · algebraic geometry
AlgebraicGeometry.isInitialOfIsEmpty
{X : AlgebraicGeometry.Scheme} → [IsEmpty ↥X] → CategoryTheory.Limits.IsInitial XA scheme is initial if its underlying space is empty .
- Defined in
- Mathlib.AlgebraicGeometry.Limits
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsEmpty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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.asIsoproof · cited by 177
- CategoryTheory.Limits.IsInitialstatement · cited by 158
- CategoryTheory.Limits.IsInitial.toproof · cited by 119
- CategoryTheory.Limits.IsInitial.ofIsoproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.exists_hom_comp_eq_comp_of_locallyOfFiniteTypeproof · cited by 2
- AlgebraicGeometry.isInitial_iff_isEmptyproof · cited by 0
- AlgebraicGeometry.Scheme.ProEt.equivOfIsEmptyproof · cited by 0