Mathlib Map

Theorems · Definition · ring theory

MonoidAlgebra.mapDomainLinearMap

(R : Type u_1) →
  (S : Type u_2) →
    {M : Type u_3} →
      {N : Type u_4} →
        [inst : Semiring R] →
          [inst_1 : Semiring S] → [inst_2 : Module R S] → (M → N) → MonoidAlgebra S M →ₗ[R] MonoidAlgebra S N

MonoidAlgebra.mapDomain as a linear map.

Defined in
Mathlib.Algebra.MonoidAlgebra.Module
Cited by
17 results in Mathlib
Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringSemiringModule

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Representation.linearize · cited by 36Representation.linearizeRepresentation.linearizeMap · cited by 15Representation.linearizeM…MonoidAlgebra.mapDomainLinearMap_single · cited by 13MonoidAlgebra.mapDomainLi…Representation.ind · cited by 7Representation.indRepresentation.linearizeMap_toLinearMap · cited by 6Representation.linearizeM…ModuleCat.monoidAlgebraFree · cited by 3ModuleCat.monoidAlgebraFr…Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq · cited by 2standardComplex.forget₂To…Representation.ind_apply · cited by 1Representation.ind_applyRepresentation.linearize_apply · cited by 1Representation.linearize_…ModuleCat.monoidAlgebraFree_map · cited by 0ModuleCat.monoidAlgebraFr…MonoidAlgebra.coeff_mapDomainLinearMap · cited by 0MonoidAlgebra.coeff_mapDo…Representation.LinearizeMonoidal.assoc_comp_δ · cited by 0LinearizeMonoidal.assoc_c…Representation.LinearizeMonoidal.lTensor_comp_δ · cited by 0LinearizeMonoidal.lTensor…Representation.LinearizeMonoidal.leftUnitor_δ · cited by 0LinearizeMonoidal.leftUni…Representation.LinearizeMonoidal.rTensor_comp_δ · cited by 0LinearizeMonoidal.rTensor…Module · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringLinearMap · cited by 10215LinearMapLinearMap.comp · cited by 1642LinearMap.compLinearEquiv.symm · cited by 1461LinearEquiv.symmLinearEquiv.toLinearMap · cited by 1171LinearEquiv.toLinearMapMonoidAlgebra · cited by 590MonoidAlgebraFinsupp.lmapDomain · cited by 63Finsupp.lmapDomainMonoidAlgebra.coeffLinearEquiv · cited by 34MonoidAlgebra.coeffLinear…MonoidAlgebra.mapDomainLinear…CITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by21

Results whose statement or proof uses this declaration.