Theorems · Theorem · commutative algebra

DividedPowerAlgebra.map_embed_apply

∀ {R : Type u_2} {M : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (S : Type u_4)
  [inst_3 : CommSemiring S] {N : Type u_5} [inst_4 : AddCommMonoid N] [inst_5 : Module R N] [inst_6 : Module S N]
  (f : M →ₗ[R] N) [inst_7 : Algebra R S] [inst_8 : IsScalarTower R S N] {m : M},
  (DividedPowerAlgebra.map S f) ((DividedPowerAlgebra.embed R M) m) = (DividedPowerAlgebra.embed S N) (f m)

Defined in

Mathlib.RingTheory.DividedPowerAlgebra.Init

Cited by

1 results in Mathlib

Foundations

Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleCommSemiringAddCommMonoidModuleModuleAlgebraIsScalarTower