id — Mathlib · SciLib

English

Defines the morphism from X_{n+1} to Z attached to a MorphComponents X n Z, combining PInfty and degeneracies.

Русский

Определяет переход от X_{n+1} к Z, ассоциированный MorphComponents X n Z, сочетая PInfty и долговороты.

LaTeX

$$$\\phi = P_\\infty^{(n+1)} \\;\\circ\\; f.a \; + \\; \\sum_{i: Fin(n+1)} (P_i).f(n+1) \\circ X.δ\\,\\text{(rev)} \\circ f.b(\\text{rev i})$$$

Lean4

/-- the canonical `MorphComponents` whose associated morphism is the identity
(see `F_id`) thanks to `decomposition_Q n (n+1)` -/
@[simps]
def id : MorphComponents X n (X _⦋n + 1⦌) where
  a := PInfty.f (n + 1)
  b i := X.σ i

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