Theorems · Definition · commutative algebra

LinearMap.finsuppLinearMap

{R : Type u_1} →
  {M : Type u_2} →
    {N : Type u_3} →
      {ι : Type u_4} →
        (S : Type u_5) →
          [inst : Semiring R] →
            [inst_1 : AddCommMonoid M] →
              [inst_2 : AddCommMonoid N] →
                [inst_3 : Module R M] →
                  [inst_4 : Module R N] →
                    [inst_5 : Semiring S] →
                      [inst_6 : Module S N] → [inst_7 : SMulCommClass R S N] → (ι →₀ M →ₗ[R] N) →ₗ[S] M →ₗ[R] ι →₀ N

The linear map from Hom(M,N)^(ι) to Hom(M,N^(ι)). This is the Finsupp version of the forward direction of LinearEquiv.linearMapPi.

Defined in

Mathlib.RingTheory.Finiteness.Finsupp

Cited by

7 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModuleSemiringModuleSMulCommClass