Theorems · Definition · group theory
powersHom
(M : Type u_1) → [inst : Monoid M] → M ≃ (Multiplicative ℕ →* M)
Monoid homomorphisms from Multiplicative ℕ are defined by the image
of Multiplicative.ofAdd 1.
- Defined in
- Mathlib.Algebra.Group.Nat.Hom
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- Monoidstatement and proof · cited by 3,887
- MonoidHomstatement · cited by 3,629
- Multiplicativestatement · cited by 875
- Additiveproof · cited by 356
- Equiv.transproof · cited by 337
- Additive.ofMulproof · cited by 155
- AddMonoidHom.toMultiplicativeLeftproof · cited by 5
- multiplesHomproof · cited by 5
Cited by10
Results whose statement or proof uses this declaration.
- Submonoid.powersproof · cited by 408
- Submonoid.powproof · cited by 13
- Polynomial.eval₂_mul_noncommproof · cited by 7
- uliftPowersHomproof · cited by 2
- powersMulHomproof · cited by 2
- Submonoid.closure_singleton_eqstatement and proof · cited by 1
- powersHom_applystatement · cited by 1
- powersHom_symm_applystatement · cited by 1
- MonoidHom.apply_mnatproof · cited by 1
- Polynomial.eval₂_ofFinsuppstatement and proof · cited by 1