toLimit — Mathlib

English

The morphism toLimit: P ⟶ limit(...) is defined as the unique morphism with a specified underlying function toLimit_fun and continuity.

Русский

Гомоморфизм toLimit: P ⟶ limit(...) задан как единственный морфизм с заданной функцией-обратной и непрерывностью.

LaTeX

$$$\mathrm{toLimit}(P) = \mathrm{ofHom}(\mathrm{toLimit\_fun}\;P)$$$

Lean4

/-- The morphism in the category of `ProfiniteGrp` from a profinite group `P` to
the projective limit of its quotients by open normal subgroups ordered by inclusion -/
def toLimit (P : ProfiniteGrp.{u}) : P ⟶ limit (toFiniteQuotientFunctor P ⋙ forget₂ FiniteGrp ProfiniteGrp) :=
  ofHom { toLimit_fun P with continuous_toFun := toLimit_fun_continuous P }

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