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 NMonoidAlgebra.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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- LinearMapstatement · cited by 10,215
- LinearMap.compproof · cited by 1,642
- LinearEquiv.symmproof · cited by 1,461
- LinearEquiv.toLinearMapproof · cited by 1,171
- MonoidAlgebrastatement · cited by 590
- Finsupp.lmapDomainproof · cited by 63
- MonoidAlgebra.coeffLinearEquivproof · cited by 34
Cited by21
Results whose statement or proof uses this declaration.
- Representation.linearizeproof · cited by 36
- Representation.linearizeMapproof · cited by 15
- MonoidAlgebra.mapDomainLinearMap_singlestatement · cited by 13
- Representation.indproof · cited by 7
- Representation.linearizeMap_toLinearMapstatement · cited by 6
- ModuleCat.monoidAlgebraFreeproof · cited by 3
- Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eqproof · cited by 2
- Representation.ind_applystatement · cited by 1
- Representation.linearize_applystatement · cited by 1
- ModuleCat.monoidAlgebraFree_mapstatement · cited by 0
- MonoidAlgebra.coeff_mapDomainLinearMapstatement · cited by 0
- Representation.LinearizeMonoidal.assoc_comp_δproof · cited by 0