initial object

noun

An object within a category which sends out arrows to all other objects in that category, and such that each of these arrows is unique.

“In the category of sets, the initial object is the empty set, since there exists a unique function, namely the empty function, from the empty set into any other given set.”

Opposite
terminal object
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Meanings

nouninitial object (plural initial objects)

plural initial objects

  1. category theoryAn object within a category which sends out arrows to all other objects in that category, and such that each of these arrows is unique.

    In the category of sets, the initial object is the empty set, since there exists a unique function, namely the empty function, from the empty set into any other given set.

Synonyms & antonyms

Opposite
terminal object

Translations

Finnish alkupiste, aluspiste
  • alkupisteTranslations
  • aluspisteTranslations
German Anfangsobjekt, initiales Objekt
  • AnfangsobjektTranslations
  • initiales ObjektTranslations
Polish obiekt początkowy
  • obiekt początkowyTranslations
Russian начальный объект
  • начальный объект (načalʹnyj obʺjekt)Translations
Cite this entry
APA

initial object. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/initial%20object

MLA

“initial object.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/initial%20object. Accessed November 2, 2026.

Chicago

WatkinsX Dictionary, s.v. “initial object,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/initial%20object.

Source: initial object on Wiktionary, CC BY-SA 4.0.