Theorems · Definition · linear algebra

Module.Dual.congr

{R : Type u_1} →
  [inst : CommSemiring R] →
    {V : Type u_2} →
      [inst_1 : AddCommMonoid V] →
        [inst_2 : Module R V] →
          {W : Type u_3} →
            [inst_3 : AddCommMonoid W] → [inst_4 : Module R W] → (V ≃ₗ[R] W) → Module.Dual R V ≃ₗ[R] Module.Dual R W

Equivalent modules have equivalent duals.

Defined in

Mathlib.LinearAlgebra.Dual.BaseChange

Cited by

4 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModule