Theorems · Theorem · ring theory

BialgHom.map_smul_of_tower

∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] [inst_5 : CoalgebraStruct R A] [inst_6 : CoalgebraStruct R B]
  (φ : A →ₐc[R] B) {R' : Type u_6} [inst_7 : SMul R' A] [inst_8 : SMul R' B] [LinearMap.CompatibleSMul A B R' R]
  (r : R') (x : A), φ (r • x) = r • φ x

Defined in

Mathlib.RingTheory.Bialgebra.Hom

Cited by

0 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebraCoalgebraStructCoalgebraStructSMulSMulLinearMap.CompatibleSMul