hσ — Mathlib

English

The family hσ' is congruent in its q-parameter: hσ'(q,n,m,a) = hσ'(q',n,m,a) when q = q'.

Русский

Семейство hσ' конгруэнтно по параметру q: hσ'(q,n,m,a) = hσ'(q',n,m,a) при q = q'.

LaTeX

$$$hσ'(q,n,m,a) = hσ'(q',n,m,a) \;\text{whenever } q = q'$$$

Lean4

/-- The sequence of maps which gives the null homotopic maps `Hσ` that shall be in
the inductive construction of the projections `P q : K[X] ⟶ K[X]` -/
def hσ (q : ℕ) (n : ℕ) : X _⦋n⦌ ⟶ X _⦋n + 1⦌ :=
  if n < q then 0 else (-1 : ℤ) ^ (n - q) • X.σ ⟨n - q, Nat.lt_succ_of_le (Nat.sub_le _ _)⟩

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