Theorems · Definition · algebraic geometry
AlgebraicGeometry.Spec.homEquiv
{R S : CommRingCat} → (AlgebraicGeometry.Spec S ⟶ AlgebraicGeometry.Spec R) ≃ (R ⟶ S)Spec is fully faithful
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- Equivstatement · cited by 8,337
- AlgebraicGeometry.Schemestatement · cited by 2,540
- CommRingCatstatement and proof · cited by 2,333
- AlgebraicGeometry.Specstatement · cited by 626
- AlgebraicGeometry.Spec.mapproof · cited by 332
- AlgebraicGeometry.Spec.preimageproof · cited by 14
- AlgebraicGeometry.Spec.map_preimageproof · cited by 11
- AlgebraicGeometry.Spec.preimage_mapproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.LocallyOfFiniteType.jacobsonSpaceproof · cited by 2
- AlgebraicGeometry.eq_of_SpecMap_comp_eq_of_isAffineOpenproof · cited by 1
- AlgebraicGeometry.isClosedMap_iff_specializingMapproof · cited by 1
- AlgebraicGeometry.Spec.homEquiv_applystatement and proof · cited by 1
- AlgebraicGeometry.Spec.homEquiv_symm_applystatement and proof · cited by 0