Theorems · Theorem · commutative algebra

Algebra.Generators.Hom.toAlgHom_comp_apply

∀ {R : Type u} {S : Type v} {ι : Type w} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  (P : Algebra.Generators R S ι) {R' : Type u_1} {S' : Type u_2} {ι' : Type u_3} [inst_3 : CommRing R']
  [inst_4 : CommRing S'] [inst_5 : Algebra R' S'] (P' : Algebra.Generators R' S' ι') {R'' : Type u_4} {S'' : Type u_5}
  {ι'' : Type u_6} [inst_6 : CommRing R''] [inst_7 : CommRing S''] [inst_8 : Algebra R'' S'']
  (P'' : Algebra.Generators R'' S'' ι'') [inst_9 : Algebra R R'] [inst_10 : Algebra R' R''] [inst_11 : Algebra R' S'']
  [inst_12 : Algebra S S'] [inst_13 : Algebra S' S''] [inst_14 : Algebra S S''] [inst_15 : Algebra R R'']
  [IsScalarTower R R' R''] [inst_17 : IsScalarTower R' R'' S''] [inst_18 : IsScalarTower R' S' S'']
  [inst_19 : IsScalarTower S S' S''] (f : P.Hom P') (g : P'.Hom P'') (x : P.Ring),
  (g.comp f).toAlgHom x = g.toAlgHom (f.toAlgHom x)

Defined in

Mathlib.RingTheory.Extension.Generators

Cited by

1 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingCommRingAlgebraCommRingCommRingAlgebraAlgebraAlgebraAlgebraAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTowerIsScalarTowerIsScalarTower