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Theorems · Theorem · group theory

DirectSum.map_surjective

∀ {ι : Type u_3} {α : ι → Type u_4} {β : ι → Type u_5} [inst : (i : ι) → AddCommMonoid (α i)]
  [inst_1 : (i : ι) → AddCommMonoid (β i)] (f : (i : ι) → α i →+ β i),
  Function.Surjective ⇑(DirectSum.map f) ↔ ∀ (i : ι), Function.Surjective ⇑(f i)
Defined in
Mathlib.Algebra.DirectSum.Basic
Cited by
0 results in Mathlib
Foundations
Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidAddCommMonoid
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DFunLike.coe · cited by 62936DFunLike.coeAddCommMonoid · cited by 12281AddCommMonoidAddMonoidHom · cited by 3230AddMonoidHommap_zero · cited by 1614map_zeroDirectSum · cited by 446DirectSumDirectSum.map · cited by 15DirectSum.mapDFinsupp.mapRange_surjective · cited by 2DFinsupp.mapRange_surject…DirectSum.map_surjectiveCITED BYCITES

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