DirectLimit — Mathlib

English

The direct limit is the quotient of the sigma-type by the setoid relation described above.

Русский

Прямой предел является фактор-мойство над Σˣ f по отношению эквивалентности.

LaTeX

$$$\\mathrm{DirectLimit} = \\Sigma_f /\\sim$ where ~ is the setoid generated by the previous equivalence.$$

Lean4

/-- The direct limit of a directed system is the structures glued together along the embeddings. -/
def DirectLimit [DirectedSystem G fun i j h => f i j h] [IsDirected ι (· ≤ ·)] :=
  Quotient (DirectLimit.setoid G f)

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