"Grothendieck universe" meaning in English

{
  "etymology_text": "Named after Alexander Grothendieck (1928–2014), a German-born French mathematician.",
  "forms": [
    {
      "form": "Grothendieck universes",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Grothendieck universe (plural Grothendieck universes)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Category theory",
          "orig": "en:Category theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "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)."
      ],
      "id": "en-Grothendieck_universe-en-noun-0h5pRocx",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "category theory",
          "category theory"
        ],
        [
          "universal set",
          "universal set"
        ]
      ],
      "raw_glosses": [
        "(mathematics, category theory) 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)."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ],
      "wikipedia": [
        "Alexander Grothendieck"
      ]
    }
  ],
  "word": "Grothendieck universe"
}

{
  "etymology_text": "Named after Alexander Grothendieck (1928–2014), a German-born French mathematician.",
  "forms": [
    {
      "form": "Grothendieck universes",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Grothendieck universe (plural Grothendieck universes)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English entries with language name categories using raw markup",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with non-redundant non-automated sortkeys",
        "en:Category theory",
        "en:Mathematics"
      ],
      "glosses": [
        "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)."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "category theory",
          "category theory"
        ],
        [
          "universal set",
          "universal set"
        ]
      ],
      "raw_glosses": [
        "(mathematics, category theory) 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)."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ],
      "wikipedia": [
        "Alexander Grothendieck"
      ]
    }
  ],
  "word": "Grothendieck universe"
}