Theorems · Theorem · algebraic geometry

AlgebraicGeometry.StructureSheaf.algebraMap_self_map

∀ (R : Type u) [inst : CommRing R] (U V : (TopologicalSpace.Opens ↑(AlgebraicGeometry.PrimeSpectrum.Top R))ᵒᵖ)
  (i : V ⟶ U),
  CategoryTheory.CategoryStruct.comp
      (CommRingCat.ofHom (algebraMap R ((AlgebraicGeometry.structureSheafInType R R).obj.obj V)))
      ((AlgebraicGeometry.Spec.structureSheaf R).obj.map i) =
    CommRingCat.ofHom (algebraMap R ((AlgebraicGeometry.structureSheafInType R R).obj.obj U))

Defined in: Mathlib.AlgebraicGeometry.StructureSheaf
Cited by: 2 results in Mathlib
Foundations: Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing

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Cites18

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
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CommRingstatement and proof · cited by 17,173
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.Functor.mapstatement · cited by 8,698
Oppositestatement and proof · cited by 8,081
Algebra.algebraMapstatement · cited by 4,706
TopCat.carrierstatement and proof · cited by 3,184
CommRingCatstatement · cited by 2,333
TopologicalSpace.Opensstatement and proof · cited by 2,040
CategoryTheory.ObjectProperty.FullSubcategory.objstatement · cited by 1,316

Cited by2

Results whose statement or proof uses this declaration.

AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_appproof · cited by 1
AlgebraicGeometry.StructureSheaf.toOpen_resproof · cited by 0