Theorems · Theorem · algebraic geometry

AlgebraicGeometry.HasAffineProperty.affineAnd_containsIdentities

∀ {Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop}
  {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme},
  AlgebraicGeometry.HasAffineProperty P (AlgebraicGeometry.affineAnd fun {R S} [CommRing R] [CommRing S] => Q) →
    (RingHom.RespectsIso fun {R S} [CommRing R] [CommRing S] => Q) →
      (RingHom.ContainsIdentities fun {R S} [CommRing R] [CommRing S] => Q) → P.ContainsIdentities

If Q contains identities and respects isomorphisms (i.e. is satisfied by isomorphisms), and P is affine locally defined by affineAnd Q, then P contains identities.

Defined in

Mathlib.AlgebraicGeometry.Morphisms.AffineAnd

Cited by

0 results in Mathlib

Foundations

Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound