Theorems · Theorem · commutative algebra

AlgHom.comp_algebraMap_of_tower

∀ (R : Type u) {S : Type v} {A : Type w} {B : Type u₁} [inst : CommSemiring R] [inst_1 : CommSemiring S]
  [inst_2 : Semiring A] [inst_3 : Semiring B] [inst_4 : Algebra R S] [inst_5 : Algebra S A] [inst_6 : Algebra S B]
  [inst_7 : Algebra R A] [inst_8 : Algebra R B] [IsScalarTower R S A] [IsScalarTower R S B] (f : A →ₐ[S] B),
  (↑f).comp (algebraMap R A) = algebraMap R B

Defined in

Mathlib.Algebra.Algebra.Tower

Cited by

23 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringSemiringSemiringAlgebraAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTower