Theorems · Definition · commutative algebra

Module.Invertible.linearEquivDual

{R : Type u} →
  {M : Type v} →
    {N : Type u_1} →
      [inst : CommSemiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : AddCommMonoid N] →
            [inst_3 : Module R M] → [inst_4 : Module R N] → (TensorProduct R M N ≃ₗ[R] R) → M ≃ₗ[R] Module.Dual R N

Given M ⊗[R] N ≃ₗ[R] R, this is the induced isomorphism M ≃ₗ[R] Nᵛ.

Defined in

Mathlib.RingTheory.PicardGroup

Cited by

1 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModule