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Theorems · Definition · linear algebra

Finsupp.curryLinearEquiv

{α : Type u_9} →
  {β : Type u_10} →
    (R : Type u_11) →
      {M : Type u_12} →
        [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → (α × β →₀ M) ≃ₗ[R] α →₀ β →₀ M

The linear equivalence between α × β →₀ M and α →₀ β →₀ M. This is the LinearEquiv version of Finsupp.curryEquiv.

Defined in
Mathlib.LinearAlgebra.Finsupp.Defs
Cited by
11 results in Mathlib
Foundations
Depth 84 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.smulTower · cited by 13Basis.smulTowerRepresentation.freeLift · cited by 5Representation.freeLiftModule.Basis.smulTower_repr · cited by 4Basis.smulTower_reprFinsupp.curryLinearEquiv_symm_apply · cited by 4Finsupp.curryLinearEquiv_…Rep.barComplex.d_single · cited by 3barComplex.d_singleFinsupp.curryLinearEquiv_apply · cited by 2Finsupp.curryLinearEquiv_…Representation.leftRegularTensorTrivialIsoFree · cited by 2Representation.leftRegula…Finsupp.curryLinearEquiv_symm_apply_apply · cited by 1Finsupp.curryLinearEquiv_…Representation.leftRegularTensorTrivialIsoFree_symm_apply_single_single · cited by 1Representation.leftRegula…Finsupp.linearCombination_smul · cited by 1Finsupp.linearCombination…Representation.freeLift_single_single · cited by 1Representation.freeLift_s…Representation.freeLift_toLinearMap · cited by 1Representation.freeLift_t…Representation.leftRegularTensorTrivialIsoFree_apply_single_tmul_single · cited by 0Representation.leftRegula…Finsupp.finsuppProdLEquiv · cited by 0Finsupp.finsuppProdLEquivFinsupp.finsuppProdLEquiv_symm_apply_apply · cited by 0Finsupp.finsuppProdLEquiv…Module · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidFinsupp · cited by 5255FinsuppLinearEquiv · cited by 3317LinearEquivAddEquiv · cited by 1087AddEquivEquiv.toFun · cited by 279Equiv.toFunAddEquiv.toEquiv · cited by 174AddEquiv.toEquivEquiv.invFun · cited by 163Equiv.invFunFinsupp.curryAddEquiv · cited by 7Finsupp.curryAddEquivFinsupp.curryLinearEquivCITED BYCITES

Cites11

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

Cited by15

Results whose statement or proof uses this declaration.