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Theorems · Definition · commutative algebra

WittVector.map

{p : ℕ} →
  {R : Type u_1} →
    {S : Type u_2} →
      [inst : CommRing R] →
        [inst_1 : CommRing S] → [inst_2 : Fact (Nat.Prime p)] → (R →+* S) → WittVector p R →+* WittVector p S

WittVector.map f is the ring homomorphism 𝕎 R →+* 𝕎 S naturally induced by a ring homomorphism f : R →+* S. It acts coefficientwise.

Defined in
Mathlib.RingTheory.WittVector.Basic
Cited by
18 results in Mathlib
Foundations
Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingFact

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

WittVector.frobeniusEquiv · cited by 9WittVector.frobeniusEquivWittVector.ghostComponentModPPow · cited by 6WittVector.ghostComponent…WittVector.fontaineThetaModPPow · cited by 5WittVector.fontaineThetaM…WittVector.map_teichmuller · cited by 3WittVector.map_teichmullerWittVector.ghostComponentModPPow_map_mk · cited by 2WittVector.ghostComponent…WittVector.ghostComponentModPPow_teichmuller_coeff · cited by 2WittVector.ghostComponent…WittVector.factorPowSucc_comp_fontaineThetaModPPow · cited by 2WittVector.factorPowSucc_…WittVector.fontaineThetaModPPow_teichmuller · cited by 1WittVector.fontaineThetaM…WittVector.ker_map_le_ker_mk_comp_ghostComponent · cited by 1WittVector.ker_map_le_ker…WittVector.quotEquivOfEq_ghostComponentModPPow · cited by 1WittVector.quotEquivOfEq_…WittVector.map_coeff · cited by 1WittVector.map_coeffWittVector.map_id · cited by 1WittVector.map_idWittVector.map_surjective · cited by 1WittVector.map_surjectiveWittVector.mk_fontaineTheta · cited by 1WittVector.mk_fontaineThe…WittVector.frobeniusEquiv_symm_apply · cited by 0WittVector.frobeniusEquiv…DFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingRingHom · cited by 10189RingHomFact · cited by 2726FactNat.Prime · cited by 2059Nat.PrimeWittVector · cited by 227WittVectorWittVector.mapFun · cited by 13WittVector.mapFunWittVector.mapFun.add · cited by 1mapFun.addWittVector.mapFun.one · cited by 1mapFun.oneWittVector.mapFun.zero · cited by 1mapFun.zeroWittVector.mapFun.mul · cited by 0mapFun.mulWittVector.mapCITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by21

Results whose statement or proof uses this declaration.