Theorems · Definition · group theory
DirectSum.of
{ι : Type v} →
(β : ι → Type w) →
[inst : (i : ι) → AddCommMonoid (β i)] → [DecidableEq ι] → (i : ι) → β i →+ DirectSum ι fun i => β iof i is the natural inclusion map from β i to ⨁ i, β i.
- Defined in
- Mathlib.Algebra.DirectSum.Basic
- Cited by
- 122 results in Mathlib
- Foundations
- Depth 31 from the axioms, rests on 413 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- AddMonoidHomstatement · cited by 3,230
- DirectSumstatement · cited by 446
- DFinsupp.singleAddHomproof · cited by 17
Cited by132
Results whose statement or proof uses this declaration.
- DirectSum.decompose_coestatement and proof · cited by 17
- DirectSum.of_eq_samestatement · cited by 12
- DirectSum.of_mul_ofstatement · cited by 11
- DirectSum.of_eq_of_nestatement · cited by 9
- DirectSum.sum_support_decomposeproof · cited by 9
- DirectSum.of_eq_of_gradedMonoid_eqstatement · cited by 8
- DirectSum.toAddMonoid_ofstatement · cited by 8
- DirectSum.decompose_of_memstatement · cited by 7
- DirectSum.decompose_symm_ofstatement · cited by 7
- DirectSum.induction_onstatement and proof · cited by 5
- DirectSum.addHom_ext'statement and proof · cited by 4
- DirectSum.coe_mul_apply_eq_dfinsuppSumproof · cited by 4