standardσ — Mathlib

English

The morphism σ is defined as the composition of degeneracy maps σ(i) in reverse order given a list L with a sum constraint m₂ + |L| = m₁.

Русский

mорфизм σ задаётся как композиция операторов обнуления σ(i) в обратном порядке согласно списку L и условию суммы.

LaTeX

$$$\\\\text{standardσ}(L) \\\\text{ with } h: m_2 + |L| = m_1 \\\\text{ is the composition } σ(i_b) \\\\\\ldots \\\\\\sigma(i_0).$$$

Lean4

/-- Given a sequence `L = [ i 0, ..., i b ]`, `standardσ m L` i is the morphism
`σ (i b) ≫ … ≫ σ (i 0)`. The construction is provided for any list of natural numbers,
but it is intended to behave well only when the list is admissible. -/
def standardσ (L : List ℕ) {m₁ m₂ : ℕ} (h : m₂ + L.length = m₁) : mk m₁ ⟶ mk m₂ :=
  match L with
  | .nil => eqToHom (by grind)
  | .cons a t => standardσ t (by grind) ≫ σ (Fin.ofNat _ a)

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