Theorems · Theorem · field theory
MonoidHom.map_frobeniusEquiv_symm
∀ {R : Type u_2} {S : Type u_3} [inst : CommSemiring R] [inst_1 : CommSemiring S] (p : ℕ) [inst_2 : ExpChar R p]
[inst_3 : PerfectRing R p] [inst_4 : ExpChar S p] [inst_5 : PerfectRing S p] (f : R →* S) (x : R),
f ((frobeniusEquiv R p).symm x) = (frobeniusEquiv S p).symm (f x)The (frobeniusEquiv R p).symm version of MonoidHom.map_frobenius.
(frobeniusEquiv R p).symm commute with any monoid homomorphisms.
- Defined in
- Mathlib.FieldTheory.Perfect
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- CommSemiringstatement and proof · cited by 10,911
- MonoidHomstatement and proof · cited by 3,629
- RingEquivstatement · cited by 1,147
- RingEquiv.symmstatement and proof · cited by 567
- Equiv.injectiveproof · cited by 464
- ExpCharstatement and proof · cited by 276
- PerfectRingstatement and proof · cited by 154
- RingEquiv.toEquivproof · cited by 101
- RingEquiv.apply_symm_applyproof · cited by 53
- frobeniusEquivstatement and proof · cited by 48
- frobenius_apply_frobeniusEquiv_symmproof · cited by 6
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.