Theorems · Definition · linear algebra

LinearMap.compAlternatingMap

{R : Type u_1} →
  [inst : Semiring R] →
    {M : Type u_2} →
      [inst_1 : AddCommMonoid M] →
        [inst_2 : Module R M] →
          {N : Type u_3} →
            [inst_3 : AddCommMonoid N] →
              [inst_4 : Module R N] →
                {ι : Type u_7} →
                  {N₂ : Type u_11} →
                    [inst_5 : AddCommMonoid N₂] →
                      [inst_6 : Module R N₂] → (N →ₗ[R] N₂) → M [⋀^ι]→ₗ[R] N → M [⋀^ι]→ₗ[R] N₂

Composing an alternating map with a linear map on the left gives again an alternating map.

Defined in

Mathlib.LinearAlgebra.Alternating.Basic

Cited by

28 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext

Assumes

SemiringAddCommMonoidModuleAddCommMonoidModuleAddCommMonoidModule