Theorems · Definition · linear algebra

AlternatingMap.curryLeft

{R : Type u_1} →
  {M : Type u_2} →
    {N : Type u_4} →
      [inst : CommSemiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : AddCommMonoid N] →
            [inst_3 : Module R M] →
              [inst_4 : Module R N] → {n : ℕ} → M [⋀^Fin n.succ]→ₗ[R] N → M →ₗ[R] M [⋀^Fin n]→ₗ[R] N

Given an alternating map f in n+1 variables, split the first variable to obtain a linear map into alternating maps in n variables, given by x ↦ (m ↦ f (Matrix.vecCons x m)). It can be thought of as a map $Hom(\bigwedge^{n+1} M, N) \to Hom(M, Hom(\bigwedge^n M, N))$. This is MultilinearMap.curryLeft for AlternatingMap. See also AlternatingMap.curryLeftLinearMap.

Defined in

Mathlib.LinearAlgebra.Alternating.Curry

Cited by

18 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModule