Theorems · Theorem · group theory
FreeAddGroup.map_surjective
∀ {α : Type u} {β : Type v} {f : α → β}, Function.Surjective f → Function.Surjective ⇑(FreeAddGroup.map f)If α and β are arbitrary types and there is a surjection between them,
then the induced map on their additive free groups is also surjective.
- Defined in
- Mathlib.GroupTheory.FreeGroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setproof · cited by 53,352
- Top.topproof · cited by 9,680
- Set.imageproof · cited by 5,609
- AddSubgroupproof · cited by 3,232
- AddMonoidHomstatement · cited by 3,230
- Set.image_univproof · cited by 322
- AddSubgroup.closureproof · cited by 156
- FreeAddGroupstatement and proof · cited by 90
- Function.Surjective.range_eqproof · cited by 70
- FreeAddGroup.ofproof · cited by 27
- AddMonoidHom.range_eq_topproof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- FreeAddGroup.map_bijectiveproof · cited by 0