factor_δ — Mathlib

English

For morphism f : [m] → [n+1] and j ∈ Fin(n+2), define factor_δ f j = f ≫ σ(Fin.predAbove 0 j). This is the factorization of f through δ_j.

Русский

Для морфизма f: [m] → [n+1] и j ∈ Fin(n+2) задано factor_δ f j = f ≫ σ(Fin.predAbove 0 j). Это факторизация через δ_j.

LaTeX

$$$\\text{factor}_{\\delta}(f,j) = f \\circ \\sigma(\\mathrm{Fin.predAbove}(0,j)).$$$

Lean4

/-- If `f : ⦋m⦌ ⟶ ⦋n+1⦌` is a morphism and `j` is not in the range of `f`,
then `factor_δ f j` is a morphism `⦋m⦌ ⟶ ⦋n⦌` such that
`factor_δ f j ≫ δ j = f` (as witnessed by `factor_δ_spec`).
-/
def factor_δ {m n : ℕ} (f : ⦋m⦌ ⟶ ⦋n + 1⦌) (j : Fin (n + 2)) : ⦋m⦌ ⟶ ⦋n⦌ :=
  f ≫ σ (Fin.predAbove 0 j)

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