Theorems · Theorem · number theory

WittVector.IsocrystalEquiv.mk.injEq

∀ {p : ℕ} [inst : Fact (Nat.Prime p)] {k : Type u_1} [inst_1 : CommRing k] [inst_2 : CharP k p]
  [inst_3 : PerfectRing k p] {V : Type u_2} [inst_4 : AddCommGroup V] [inst_5 : WittVector.Isocrystal p k V]
  {V₂ : Type u_3} [inst_6 : AddCommGroup V₂] [inst_7 : WittVector.Isocrystal p k V₂]
  (toLinearEquiv : V ≃ₗ[FractionRing (WittVector p k)] V₂)
  (frob_equivariant :
    ∀ (x : V),
      (WittVector.Isocrystal.frobenius p k) (toLinearEquiv x) = toLinearEquiv ((WittVector.Isocrystal.frobenius p k) x))
  (toLinearEquiv_1 : V ≃ₗ[FractionRing (WittVector p k)] V₂)
  (frob_equivariant_1 :
    ∀ (x : V),
      (WittVector.Isocrystal.frobenius p k) (toLinearEquiv_1 x) =
        toLinearEquiv_1 ((WittVector.Isocrystal.frobenius p k) x)),
  ({ toLinearEquiv := toLinearEquiv, frob_equivariant := frob_equivariant } =
      { toLinearEquiv := toLinearEquiv_1, frob_equivariant := frob_equivariant_1 }) =
    (toLinearEquiv = toLinearEquiv_1)

Defined in

Mathlib.RingTheory.WittVector.Isocrystal

Cited by

0 results in Mathlib

Foundations

Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FactCommRingCharPPerfectRingAddCommGroupWittVector.IsocrystalAddCommGroupWittVector.Isocrystal