Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.GlueData.isoCarrier
(D : AlgebraicGeometry.Scheme.GlueData) →
↑D.glued.toPresheafedSpace ≅
D.toLocallyRingedSpaceGlueData.toSheafedSpaceGlueData.toPresheafedSpaceGlueData.toTopGlueData.gluedThe underlying topological space of the glued scheme is isomorphic to the gluing of the underlying spaces
- Defined in
- Mathlib.AlgebraicGeometry.Gluing
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Isostatement · cited by 3,963
- CommRingCatstatement and proof · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- TopCatstatement · cited by 1,889
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- CategoryTheory.Iso.transproof · cited by 566
- CategoryTheory.Functor.mapIsoproof · cited by 224
- CategoryTheory.Limits.WalkingMultispanstatement · cited by 151
- CategoryTheory.GlueData.Jstatement · cited by 141
- CategoryTheory.Limits.MultispanIndex.multispanstatement · cited by 139
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.GlueData.ι_eq_iffproof · cited by 2
- AlgebraicGeometry.Scheme.GlueData.ι_isoCarrier_invstatement · cited by 2
- AlgebraicGeometry.Scheme.GlueData.isOpen_iffproof · cited by 1