Theorems · Theorem · commutative algebra

PerfectionMap.map_map

∀ (p : ℕ) [inst : Fact (Nat.Prime p)] {R : Type u₁} [inst_1 : CommSemiring R] [inst_2 : CharP R p] {P : Type u₃}
  [inst_3 : CommSemiring P] [inst_4 : CharP P p] [inst_5 : PerfectRing P p] {S : Type u₂} [inst_6 : CommSemiring S]
  [inst_7 : CharP S p] {Q : Type u₄} [inst_8 : CommSemiring Q] [inst_9 : CharP Q p] [inst_10 : PerfectRing Q p]
  {π : P →+* R} (m : PerfectionMap p π) {σ : Q →+* S} (n : PerfectionMap p σ) (φ : R →+* S) (x : P),
  σ ((PerfectionMap.map p m n φ) x) = φ (π x)

Defined in

Mathlib.RingTheory.Perfection

Cited by

1 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FactCommSemiringCharPCommSemiringCharPPerfectRingCommSemiringCharPCommSemiringCharPPerfectRing