Theorems · Definition · algebraic geometry
AlgebraicGeometry.Spec.topMap
{R S : CommRingCat} → (R ⟶ S) → (AlgebraicGeometry.Spec.topObj S ⟶ AlgebraicGeometry.Spec.topObj R)The induced map of a ring homomorphism on the ring spectra, as a morphism of topological spaces.
- Defined in
- Mathlib.AlgebraicGeometry.Spec
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CommRingCatstatement and proof · cited by 2,333
- TopCatstatement · cited by 1,889
- CommRingCat.Hom.homproof · cited by 432
- PrimeSpectrum.comapproof · cited by 199
- TopCat.ofHomproof · cited by 44
- AlgebraicGeometry.Spec.topObjstatement · cited by 17
Cited by17
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Spec.sheafedSpaceMapproof · cited by 16
- AlgebraicGeometry.StructureSheaf.toPushforwardStalkstatement and proof · cited by 3
- AlgebraicGeometry.StructureSheaf.toPushforwardStalkAlgHomstatement and proof · cited by 2
- AlgebraicGeometry.Spec.sheafedSpaceMap_hom_c_appstatement · cited by 2
- AlgebraicGeometry.Spec.toTopproof · cited by 2
- AlgebraicGeometry.StructureSheaf.algebraMap_pushforward_stalkstatement · cited by 1
- AlgebraicGeometry.StructureSheaf.toPushforwardStalk_compstatement and proof · cited by 1
- AlgebraicGeometry.Spec_Γ_naturalityproof · cited by 1
- AlgebraicGeometry.Spec.sheafedSpaceMap_compproof · cited by 1
- AlgebraicGeometry.stalkMap_toStalkproof · cited by 1
- AlgebraicGeometry.Spec.topMap_compstatement · cited by 1
- AlgebraicGeometry.Spec.topMap_idstatement · cited by 1