Theorems · Definition · linear algebra

exteriorPower.alternatingMapLinearEquiv

{R : Type u} →
  [inst : CommRing R] →
    {n : ℕ} →
      {M : Type u_1} →
        {N : Type u_2} →
          [inst_1 : AddCommGroup M] →
            [inst_2 : Module R M] →
              [inst_3 : AddCommGroup N] → [inst_4 : Module R N] → M [⋀^Fin n]→ₗ[R] N ≃ₗ[R] ↥(⋀[R]^n M) →ₗ[R] N

The linear equivalence between n-fold alternating maps from M to N and linear maps from ⋀[R]^n M to N: this is the universal property of the nth exterior power of M.

Defined in

Mathlib.LinearAlgebra.ExteriorPower.Basic

Cited by

6 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule