Theorems · Definition · group theory
FreeGroup.map
{α : Type u} → {β : Type v} → (α → β) → FreeGroup α →* FreeGroup βAny function from α to β extends uniquely to a group homomorphism from the free group over
α to the free group over β.
- Defined in
- Mathlib.GroupTheory.FreeGroup.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MonoidHomstatement · cited by 3,629
- FreeGroupstatement · cited by 132
- FreeGroup.Red.Stepproof · cited by 43
- Quot.mapproof · cited by 5
- MonoidHom.mk'proof · cited by 3
Cited by25
Results whose statement or proof uses this declaration.
- FreeGroup.freeGroupCongrproof · cited by 8
- FreeGroup.map.idstatement · cited by 3
- FreeGroup.map.compstatement · cited by 2
- FreeGroup.freeGroupUnitEquivIntproof · cited by 1
- FreeGroup.map_surjectivestatement · cited by 1
- FreeGroup.freeGroupCongr_applystatement · cited by 1
- FreeGroup.range_mapstatement · cited by 1
- PresentedGroup.lift_toCoprod_inl_eq_inl_mkstatement and proof · cited by 1
- PresentedGroup.lift_toCoprod_inr_eq_inr_mkstatement and proof · cited by 1
- FreeGroup.map_eq_liftstatement and proof · cited by 1
- FreeGroup.map_injectivestatement and proof · cited by 1
- FreeGroup.map.ofstatement · cited by 1