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Definitions of direct limit:
  • noun:   (algebra) A set of equivalence classes which partition the disjoint union of the members of a direct system; each equivalence class being a sort of “drainage basin” of the mappings (of the morphisms) of the direct system, if these are analogically considered as “rivers”. (If inoun:   (category theory) a colimit

(Definitions from Wiktionary)

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