Theorems · Theorem · algebraic geometry

Algebra.IsLocalIso.trans

∀ (R : Type u_1) (S : Type u_2) [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S] (T : Type u_3)
  [inst_3 : CommSemiring T] [inst_4 : Algebra S T] [inst_5 : Algebra R T] [IsScalarTower R S T] [Algebra.IsLocalIso R S]
  [Algebra.IsLocalIso S T], Algebra.IsLocalIso R T

Local isomorphisms are stable under composition.

Defined in: Mathlib.RingTheory.LocalIso
Cited by: 1 results in Mathlib
Foundations: Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring CommSemiring Algebra CommSemiring Algebra Algebra IsScalarTower Algebra.IsLocalIso Algebra.IsLocalIso

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Cites40

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

DFunLike.coeproof · cited by 62,936
Setproof · cited by 53,352
Algebrastatement and proof · cited by 11,388
CommSemiringstatement and proof · cited by 10,911
Top.topproof · cited by 9,680
Set.Elemproof · cited by 7,166
Set.ofPredproof · cited by 6,101
Set.imageproof · cited by 5,609
Idealproof · cited by 4,748
Algebra.algebraMapproof · cited by 4,706
Set.rangeproof · cited by 4,705
IsScalarTowerstatement and proof · cited by 3,896

Cited by1

Results whose statement or proof uses this declaration.

Algebra.IsLocalIso.of_algEquivproof · cited by 1