"hom-set" meaning in All languages combined

See hom-set on Wiktionary

Noun [English]

Forms: hom-sets [plural]
Etymology: Short for "homomorphism set", because in some categories the morphisms are homomorphisms. Head templates: {{en-noun}} hom-set (plural hom-sets)
  1. (category theory) The set or collection of all morphisms from A to B for some given ordered pair (A, B) of objects from some given category. Categories (topical): Category theory Synonyms: morphism set

Inflected forms

{
  "etymology_text": "Short for \"homomorphism set\", because in some categories the morphisms are homomorphisms.",
  "forms": [
    {
      "form": "hom-sets",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "hom-set (plural hom-sets)",
      "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": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Category theory",
          "orig": "en:Category theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "The set or collection of all morphisms from A to B for some given ordered pair (A, B) of objects from some given category."
      ],
      "id": "en-hom-set-en-noun-zA8Pn15b",
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "morphism",
          "morphism"
        ],
        [
          "object",
          "object"
        ]
      ],
      "raw_glosses": [
        "(category theory) The set or collection of all morphisms from A to B for some given ordered pair (A, B) of objects from some given category."
      ],
      "synonyms": [
        {
          "word": "morphism set"
        }
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    }
  ],
  "word": "hom-set"
}
{
  "etymology_text": "Short for \"homomorphism set\", because in some categories the morphisms are homomorphisms.",
  "forms": [
    {
      "form": "hom-sets",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "hom-set (plural hom-sets)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Category theory"
      ],
      "glosses": [
        "The set or collection of all morphisms from A to B for some given ordered pair (A, B) of objects from some given category."
      ],
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "morphism",
          "morphism"
        ],
        [
          "object",
          "object"
        ]
      ],
      "raw_glosses": [
        "(category theory) The set or collection of all morphisms from A to B for some given ordered pair (A, B) of objects from some given category."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "morphism set"
    }
  ],
  "word": "hom-set"
}

Download raw JSONL data for hom-set meaning in All languages combined (1.1kB)


This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.