Theorems · Theorem · commutative algebra

QuotSMulTop.equivTensorQuot_naturality

∀ {R : Type u_2} [inst : CommRing R] (r : R) {M : Type u_1} {M' : Type u_3} [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] [inst_3 : AddCommGroup M'] [inst_4 : Module R M'] (f : M →ₗ[R] M'),
  ↑(QuotSMulTop.equivTensorQuot r M') ∘ₗ (QuotSMulTop.map r) f =
    LinearMap.rTensor (R ⧸ Ideal.span {r}) f ∘ₗ ↑(QuotSMulTop.equivTensorQuot r M)

Defined in

Mathlib.RingTheory.QuotSMulTop

Cited by

0 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule