Theorems · Theorem · commutative algebra

PolynomialLaw.isCompat_apply

∀ {R : Type u} [inst : CommSemiring R] {M : Type u_1} [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {N : Type u_2}
  [inst_3 : AddCommMonoid N] [inst_4 : Module R N] {S : Type v} [inst_5 : CommSemiring S] [inst_6 : Algebra R S]
  (f : M →ₚₗ[R] N) {T : Type w} [inst_7 : CommSemiring T] [inst_8 : Algebra R T] (h : S →ₐ[R] T)
  (t : TensorProduct R S M),
  (LinearMap.rTensor N h.toLinearMap) (PolynomialLaw.toFun S f t) =
    PolynomialLaw.toFun T f ((LinearMap.rTensor M h.toLinearMap) t)

Extends PolynomialLaw.isCompat_apply' to all universes.

Defined in

Mathlib.RingTheory.PolynomialLaw.Basic

Cited by

2 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleCommSemiringAlgebraCommSemiringAlgebra