Theorems · Definition · group theory
DirectSum.coeFnAddMonoidHom
{ι : Type v} → (β : ι → Type w) → [inst : (i : ι) → AddCommMonoid (β i)] → (DirectSum ι fun i => β i) →+ (i : ι) → β iCoercion from a DirectSum to a pi type is an AddMonoidHom.
- Defined in
- Mathlib.Algebra.DirectSum.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 31 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- AddMonoidHomstatement and proof · cited by 3,230
- DFinsuppproof · cited by 694
- DirectSumstatement and proof · cited by 446
- DFinsupp.coeFnAddMonoidHomproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- DirectSum.mker_mapstatement · cited by 0
- DirectSum.mrange_mapstatement · cited by 0
- DirectSum.coeFnAddMonoidHom_applystatement · cited by 0
- DirectSum.range_mapstatement · cited by 0
- DirectSum.ker_mapstatement · cited by 0