Grothendieck universe

noun

A kind of universal set whose elements follow the rules of Zermelo–Fraenkel set theory, and for which, with respect to an arbitrary set, an instance of its kind which has that set as a member may be posited to exist through an additional Tarski–Grothendieck axiom (which is not part of ZF but augments it, yielding Tarski–Grothendieck set theory).

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Meanings

nounGrothendieck universe (plural Grothendieck universes)

plural Grothendieck universes

  1. category theoryA kind of universal set whose elements follow the rules of Zermelo–Fraenkel set theory, and for which, with respect to an arbitrary set, an instance of its kind which has that set as a member may be posited to exist through an additional Tarski–Grothendieck axiom (which is not part of ZF but augments it, yielding Tarski–Grothendieck set theory).

Origin

Named after Alexander Grothendieck (1928–2014), a German-born French mathematician.

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Cite this entry
APA

Grothendieck universe. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Grothendieck%20universe

MLA

“Grothendieck universe.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Grothendieck%20universe. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Grothendieck universe,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Grothendieck%20universe.

Source: Grothendieck universe on Wiktionary, CC BY-SA 4.0.