Theorems · Definition · algebraic geometry
AlgebraicGeometry.IsClosedImmersion.overEquivIdealSheafData
(X : AlgebraicGeometry.Scheme) → (CategoryTheory.MorphismProperty.Over @AlgebraicGeometry.IsClosedImmersion ⊤ X)ᵒᵖ ≌ X.IdealSheafData
The category of closed subschemes is contravariantly equivalent to the lattice of ideal sheaves.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- Top.topstatement and proof · cited by 9,680
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.Functor.idstatement · cited by 3,333
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.Discretestatement · cited by 2,447
- Opposite.unopproof · cited by 2,231
- CategoryTheory.MorphismPropertystatement · cited by 2,179
- Quiver.Hom.opproof · cited by 1,948
- CategoryTheory.Functor.opproof · cited by 997
- CategoryTheory.Iso.symmproof · cited by 993
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsClosedImmersion.isIso_of_ker_eqproof · cited by 2