Theorems · Definition · algebraic geometry

AlgebraicGeometry.HasRingHomProperty.casesOn

{P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} →
  {Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop} →
    {motive : AlgebraicGeometry.HasRingHomProperty P Q → Sort u_1} →
      (t : AlgebraicGeometry.HasRingHomProperty P Q) →
        ((isLocal_ringHomProperty : RingHom.PropertyIsLocal fun {R S} [CommRing R] [CommRing S] => Q) →
            (eq_affineLocally' : P = AlgebraicGeometry.affineLocally fun {R S} [CommRing R] [CommRing S] => Q) →
              motive ⋯) →
          motive t

Defined in: Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties
Cited by: 0 results in Mathlib
Foundations: Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound

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CommRingstatement and proof · cited by 17,173
RingHomstatement and proof · cited by 10,189
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
AlgebraicGeometry.HasRingHomPropertystatement and proof · cited by 38
RingHom.PropertyIsLocalstatement and proof · cited by 20
AlgebraicGeometry.affineLocallystatement and proof · cited by 13

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