Theorems · Theorem · algebraic geometry

RingHom.SurjectiveOnStalks.tensorProductMap

∀ {R : Type u_1} [inst : CommRing R] {S : Type u_2} [inst_1 : CommRing S] {T : Type u_3} [inst_2 : CommRing T]
  {S' : Type u_4} {T' : Type u_5} [inst_3 : CommRing S'] [inst_4 : CommRing T'] [inst_5 : Algebra R S]
  [inst_6 : Algebra R T] [inst_7 : Algebra R S'] [inst_8 : Algebra R T'] {f : S →ₐ[R] S'},
  f.SurjectiveOnStalks → ∀ {g : T →ₐ[R] T'}, g.SurjectiveOnStalks → (Algebra.TensorProduct.map f g).SurjectiveOnStalks

Defined in

Mathlib.RingTheory.SurjectiveOnStalks

Cited by

0 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingCommRingCommRingAlgebraAlgebraAlgebraAlgebra