smaller — Mathlib

English

There is a commutative diagram linking smaller and bigger GoodProducts via πs projections.

Русский

Существует диаграмма перехода между меньшими и большими GoodProducts через проекции πs.

LaTeX

$$$$\\mathrm{smaller\\_factorization}(C) : (\\text{…}) = (\\mathrm{πs}\\; C \\; o) \\circ (\\mathrm{range}\\; (\\mathrm{π}\\; C))$$$$

Lean4

/-- The image of the `GoodProducts` for `π C (ord I · < o)` in `LocallyConstant C ℤ`. The name `smaller`
refers to the setting in which we will use this, when we are mapping in `GoodProducts` from a
smaller set, i.e. when `o` is a smaller ordinal than the one `C` is "contained" in.
-/
def smaller (o : Ordinal) : Set (LocallyConstant C ℤ) :=
  (πs C o) '' (range (π C (ord I · < o)))

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