Mathlib Map

Theorems · Definition · linear algebra

Finsupp.lapply

{α : Type u_1} →
  {M : Type u_2} →
    {R : Type u_5} → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → α → (α →₀ M) →ₗ[R] M

Interpret fun f : α →₀ M ↦ f a as a linear map.

Defined in
Mathlib.LinearAlgebra.Finsupp.Defs
Cited by
19 results in Mathlib
Foundations
Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringAddCommMonoidModule

Around this declaration

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

Module.Basis.coord · cited by 64Basis.coordlinearIndependent_iff'ₛ · cited by 9linearIndependent_iff'ₛKaehlerDifferential.mvPolynomialBasis_repr_apply · cited by 2KaehlerDifferential.mvPol…Module.Basis.repr_apply_eq · cited by 2Basis.repr_apply_eqFinsupp.lapply_apply · cited by 2Finsupp.lapply_applyModuleCat.FreeMonoidal.εIso · cited by 2FreeMonoidal.εIsoLinearMap.finsuppLinearMap_bijective_of_finite · cited by 1LinearMap.finsuppLinearMa…LinearMap.finsuppLinearMap_bijective_of_moduleFinite · cited by 1LinearMap.finsuppLinearMa…Finsupp.iInf_ker_lapply_le_bot · cited by 1Finsupp.iInf_ker_lapply_l…Finsupp.lsingle_range_le_ker_lapply · cited by 1Finsupp.lsingle_range_le_…Finsupp.lapply_comp_lsingle_of_ne · cited by 1Finsupp.lapply_comp_lsing…Finsupp.lapply_comp_lsingle_same · cited by 1Finsupp.lapply_comp_lsing…TensorProduct.finsuppLeft_apply · cited by 1TensorProduct.finsuppLeft…eq_bot_of_generator_maximal_submoduleImage_eq_zero · cited by 1eq_bot_of_generator_maxim…TensorProduct.finsuppRight_apply · cited by 1TensorProduct.finsuppRigh…Module · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidLinearMap · cited by 10215LinearMapFinsupp · cited by 5255FinsuppAddMonoidHom · cited by 3230AddMonoidHomZeroHom.toFun · cited by 101ZeroHom.toFunAddMonoidHom.toZeroHom · cited by 61AddMonoidHom.toZeroHomFinsupp.applyAddHom · cited by 3Finsupp.applyAddHomFinsupp.lapplyCITED 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.