Theorems · Theorem · group theory
powMonoidHom_apply
∀ {α : Type u_1} [inst : CommMonoid α] (n : ℕ) (x : α), (powMonoidHom n) x = x ^ n- Defined in
- Mathlib.Algebra.Group.Hom.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- MonoidHomstatement · cited by 3,629
- CommMonoidstatement and proof · cited by 2,264
- powMonoidHomstatement and proof · cited by 35
Cited by11
Results whose statement or proof uses this declaration.
- MvPolynomial.map_frobenius_expandproof · cited by 2
- CommGroup.isMulTorsion_quotient_range_powMonoidHomproof · cited by 2
- NumberField.IsCMField.index_unitsMulComplexConjInv_range_dvdproof · cited by 1
- IsDedekindDomain.selmerGroup.fromUnit_kerproof · cited by 1
- NumberField.IsCMField.map_unitsMulComplexConjInv_torsionproof · cited by 1
- IsCyclic.card_powMonoidHom_rangeproof · cited by 1
- isQuotientCoveringMap_zpowproof · cited by 0
- exists_isTranscendenceBasis_and_isSeparable_of_perfectFieldproof · cited by 0
- Subgroup.isFiniteRelIndex_map_powMonoidHom_of_fgproof · cited by 0
- Subgroup.subgroupOf_map_powMonoidHom_eq_rangeproof · cited by 0
- MulEquiv.map_range_powMonoidHomproof · cited by 0