Theorems · Definition · group theory
DirectSum.id
(M : Type v) →
(ι : optParam (Type u_1) PUnit.{u_1 + 1}) → [inst : AddCommMonoid M] → [Unique ι] → (DirectSum ι fun x => M) ≃+ MThe natural equivalence between ⨁ _ : ι, M and M when Unique ι.
- Defined in
- Mathlib.Algebra.DirectSum.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidUnique
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- AddMonoidHomproof · cited by 3,230
- AddEquivstatement · cited by 1,087
- DirectSumstatement and proof · cited by 446
- Uniquestatement and proof · cited by 400
- DirectSum.ofproof · cited by 122
- AddMonoidHom.idproof · cited by 107
- DirectSum.toAddMonoidproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- DirectSum.id_symm_applystatement · cited by 2
- DirectSum.lidproof · cited by 2
- DirectSum.id_applystatement and proof · cited by 1