Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpec

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) {V : X.Opens} {U : Y.Opens} (hU : AlgebraicGeometry.IsAffineOpen U)
  (hV : AlgebraicGeometry.IsAffineOpen V) (i : V ≤ (TopologicalSpace.Opens.map f.base).obj U),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Spec.map (AlgebraicGeometry.Scheme.Hom.appLE f U V i))
      hU.fromSpec =
    CategoryTheory.CategoryStruct.comp hV.fromSpec f

Defined in: Mathlib.AlgebraicGeometry.AffineScheme
Cited by: 8 results in Mathlib
Foundations: Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites56

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 and proof · cited by 19,642
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
Top.topproof · cited by 9,680
CategoryTheory.Functor.mapproof · cited by 8,698
Oppositestatement · cited by 8,081
CategoryTheory.Iso.invproof · cited by 6,514
CategoryTheory.Category.assocproof · cited by 6,433
TopCat.carrierstatement · cited by 3,184
LE.le.transproof · cited by 3,151
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CommRingCatstatement · cited by 2,333

Cited by8

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalkproof · cited by 8
AlgebraicGeometry.Scheme.Hom.normalizationDesc_compproof · cited by 5
AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalkproof · cited by 3
AlgebraicGeometry.spread_out_of_isGermInjectiveproof · cited by 1
AlgebraicGeometry.exists_etale_isCompl_of_quasiFiniteAtproof · cited by 1
AlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpec_assocproof · cited by 1
AlgebraicGeometry.FormallyUnramified.of_hom_extproof · cited by 0
AlgebraicGeometry.Scheme.Hom.normalization.hom_extproof · cited by 0