Theorems · Definition · algebraic geometry
AlgebraicGeometry.Spec.toLocallyRingedSpace
CategoryTheory.Functor CommRingCatᵒᵖ AlgebraicGeometry.LocallyRingedSpace
Spec, as a contravariant functor from commutative rings to locally ringed spaces.
- Defined in
- Mathlib.AlgebraicGeometry.Spec
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 126 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.Homproof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- CommRingCatstatement and proof · cited by 2,333
- Opposite.unopproof · cited by 2,231
- Quiver.Hom.unopproof · cited by 903
- AlgebraicGeometry.LocallyRingedSpacestatement · cited by 205
- AlgebraicGeometry.Spec.locallyRingedSpaceObjproof · cited by 57
- AlgebraicGeometry.Spec.locallyRingedSpaceMapproof · cited by 7
Cited by42
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.affineCoverproof · cited by 61
- AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunctionstatement · cited by 11
- AlgebraicGeometry.toSpecΓstatement · cited by 8
- AlgebraicGeometry.identityToΓSpecstatement · cited by 5
- AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentitystatement · cited by 5
- AlgebraicGeometry.Scheme.local_affinestatement · cited by 3
- AlgebraicGeometry.Scheme.exists_affine_mem_range_and_range_subsetproof · cited by 2
- AlgebraicGeometry.Scheme.mk.injstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.mk.noConfusionstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.affineBasisCover_map_rangestatement · cited by 1
- AlgebraicGeometry.LocallyRingedSpace.Γ_Spec_left_trianglestatement and proof · cited by 1
- AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_appstatement and proof · cited by 1