Theorems · Theorem · group theory
FreeGroup.ext_hom
∀ {α : Type u} {M : Type u_1} [inst : Monoid M] (f g : FreeGroup α →* M),
(∀ (a : α), f (FreeGroup.of a) = g (FreeGroup.of a)) → f = gTwo homomorphisms out of a free group are equal if they are equal on generators. See note [partially-applied ext lemmas].
- Defined in
- Mathlib.GroupTheory.FreeGroup.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Monoidstatement and proof · cited by 3,887
- mul_oneproof · cited by 3,885
- MonoidHomstatement and proof · cited by 3,629
- one_mulproof · cited by 2,841
- mul_assocproof · cited by 1,667
- map_mulproof · cited by 1,137
- map_oneproof · cited by 861
- FreeGroupstatement and proof · cited by 132
- mul_inv_cancelproof · cited by 128
- MonoidHom.extproof · cited by 109
- inv_mul_cancelproof · cited by 107
Cited by6
Results whose statement or proof uses this declaration.
- PresentedGroup.lift_toCoprod_inl_eq_inl_mkproof · cited by 1
- PresentedGroup.lift_toCoprod_inr_eq_inr_mkproof · cited by 1
- FreeGroup.map_eq_liftproof · cited by 1
- PresentedGroup.extproof · cited by 1
- FreeGroup.injective_lift_of_ping_pongproof · cited by 0
- FreeGroup.ext_hom_iffproof · cited by 0