Mathlib Map

Theorems · Theorem · commutative algebra

Algebra.IsStandardSmooth.trans

∀ (R : Type u) (S : Type v) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (T : Type u_1)
  [inst_3 : CommRing T] [inst_4 : Algebra R T] [inst_5 : Algebra S T] [IsScalarTower R S T]
  [Algebra.IsStandardSmooth R S] [Algebra.IsStandardSmooth S T], Algebra.IsStandardSmooth R T
Defined in
Mathlib.RingTheory.Smooth.StandardSmooth
Cited by
1 results in Mathlib
Foundations
Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTowerAlgebra.IsStandardSmoothAlgebra.IsStandardSmooth
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

RingHom.IsStandardSmooth.comp · cited by 1IsStandardSmooth.compCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraIsScalarTower · cited by 3896IsScalarTowerFinite · cited by 3029FiniteAlgebra.SubmersivePresentation · cited by 52Algebra.SubmersivePresent…Algebra.IsStandardSmooth · cited by 17Algebra.IsStandardSmoothAlgebra.IsStandardSmooth.casesOn · cited by 4IsStandardSmooth.casesOnAlgebra.SubmersivePresentation.comp · cited by 2SubmersivePresentation.co…IsStandardSmooth.transCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.