Theorems · Definition · group theory
FreeAbelianGroup.liftMonoid
{α : Type u} → {R : Type u_2} → [inst : Monoid α] → [inst_1 : Ring R] → (α →* R) ≃ (FreeAbelianGroup α →+* R)If f preserves multiplication, then so does lift f.
- Defined in
- Mathlib.GroupTheory.FreeAbelianGroup
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- Equivstatement · cited by 8,337
- Ringstatement and proof · cited by 7,463
- Monoidstatement and proof · cited by 3,887
- MonoidHomstatement and proof · cited by 3,629
- AddMonoidHomproof · cited by 3,230
- MonoidHom.compproof · cited by 469
- MonoidHomClass.toMonoidHomproof · cited by 294
- FreeAbelianGroupstatement and proof · cited by 82
- FreeAbelianGroup.liftproof · cited by 33
- FreeAbelianGroup.ofMulHomproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- FreeCommRing.liftproof · cited by 10
- FreeRing.liftproof · cited by 6
- FreeAbelianGroup.liftMonoid_coestatement · cited by 0
- FreeAbelianGroup.liftMonoid_coe_addMonoidHomstatement · cited by 0
- FreeAbelianGroup.liftMonoid_symm_coestatement · cited by 0