Theorems · Definition · group theory
FreeAbelianGroup.lift
{α : Type u} → {β : Type v} → [inst : AddCommGroup β] → (α → β) ≃ (FreeAbelianGroup α →+ β)The map FreeAbelianGroup α →+ A induced by a map of types α → A.
- Defined in
- Mathlib.GroupTheory.FreeAbelianGroup
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- Equivstatement · cited by 8,337
- AddMonoidHomstatement · cited by 3,230
- Equiv.transproof · cited by 337
- FreeAbelianGroupstatement · cited by 82
- FreeGroup.liftproof · cited by 32
- MonoidHom.toAdditiveproof · cited by 19
- Abelianization.liftproof · cited by 9
Cited by40
Results whose statement or proof uses this declaration.
- FreeAbelianGroup.lift_apply_ofstatement and proof · cited by 12
- FreeAbelianGroup.toFinsuppproof · cited by 10
- FreeAbelianGroup.mapproof · cited by 7
- FreeAbelianGroup.of_injectiveproof · cited by 6
- FreeAbelianGroup.lift_extproof · cited by 4
- FreeAbelianGroup.liftAddEquivproof · cited by 3
- FreeAbelianGroup.liftMonoidproof · cited by 3
- FreeAbelianGroup.lift_uniquestatement and proof · cited by 3
- FreeAbelianGroup.of_ne_zeroproof · cited by 3
- FreeAbelianGroup.of_mul_ofproof · cited by 2
- FreeAbelianGroup.sub_bindproof · cited by 1
- FreeAbelianGroup.zero_bindproof · cited by 1