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 MThe 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Finsuppstatement and proof · cited by 5,255
- LinearEquivstatement · cited by 3,317
- AddEquivproof · cited by 1,087
- Equiv.toFunproof · cited by 279
- AddEquiv.toEquivproof · cited by 174
- Equiv.invFunproof · cited by 163
- Finsupp.curryAddEquivproof · cited by 7
Cited by15
Results whose statement or proof uses this declaration.
- Module.Basis.smulTowerproof · cited by 13
- Representation.freeLiftproof · cited by 5
- Module.Basis.smulTower_reprproof · cited by 4
- Finsupp.curryLinearEquiv_symm_applystatement and proof · cited by 4
- Rep.barComplex.d_singleproof · cited by 3
- Finsupp.curryLinearEquiv_applystatement and proof · cited by 2
- Representation.leftRegularTensorTrivialIsoFreeproof · cited by 2
- Finsupp.curryLinearEquiv_symm_apply_applystatement · cited by 1
- Representation.leftRegularTensorTrivialIsoFree_symm_apply_single_singleproof · cited by 1
- Finsupp.linearCombination_smulstatement · cited by 1
- Representation.freeLift_single_singleproof · cited by 1
- Representation.freeLift_toLinearMapstatement · cited by 1