Theorems · Theorem · ring theory
SkewMonoidAlgebra.mapDomain_apply
∀ {k : Type u_1} {G : Type u_2} [inst : AddCommMonoid k] {G' : Type u_3} (f : G → G') (v : SkewMonoidAlgebra k G),
(SkewMonoidAlgebra.mapDomain f) v = v.sum fun a => SkewMonoidAlgebra.single (f a)- Defined in
- Mathlib.Algebra.SkewMonoidAlgebra.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- AddMonoidHomstatement · cited by 3,230
- SkewMonoidAlgebrastatement and proof · cited by 216
- SkewMonoidAlgebra.singlestatement · cited by 83
- SkewMonoidAlgebra.sumstatement · cited by 46
- SkewMonoidAlgebra.mapDomainstatement and proof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- SkewMonoidAlgebra.coeff_mapDomainproof · cited by 3
- SkewMonoidAlgebra.mapDomain_mulproof · cited by 0