"slice category" meaning in All languages combined

See slice category on Wiktionary

Noun [English]

Forms: slice categories [plural]
Head templates: {{en-noun}} slice category (plural slice categories)
  1. (category theory) A category whose objects are morphisms (of some given category) with a common codomain, and whose morphisms are commuting triangles where two morphisms of each of such triangles share the said common codomain. Categories (topical): Category theory Synonyms: overcategory Hypernyms: comma category

Inflected forms

Download JSON data for slice category meaning in All languages combined (1.4kB)

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  "antonyms": [
    {
      "word": "coslice category"
    }
  ],
  "forms": [
    {
      "form": "slice categories",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "slice category (plural slice categories)",
      "name": "en-noun"
    }
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  "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": "topical",
          "langcode": "en",
          "name": "Category theory",
          "orig": "en:Category theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A category whose objects are morphisms (of some given category) with a common codomain, and whose morphisms are commuting triangles where two morphisms of each of such triangles share the said common codomain."
      ],
      "hypernyms": [
        {
          "word": "comma category"
        }
      ],
      "id": "en-slice_category-en-noun-SDZcEqAz",
      "links": [
        [
          "category theory",
          "category theory"
        ]
      ],
      "raw_glosses": [
        "(category theory) A category whose objects are morphisms (of some given category) with a common codomain, and whose morphisms are commuting triangles where two morphisms of each of such triangles share the said common codomain."
      ],
      "synonyms": [
        {
          "word": "overcategory"
        }
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    }
  ],
  "word": "slice category"
}
{
  "antonyms": [
    {
      "word": "coslice category"
    }
  ],
  "forms": [
    {
      "form": "slice categories",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "slice category (plural slice categories)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "comma category"
    }
  ],
  "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",
        "en:Category theory"
      ],
      "glosses": [
        "A category whose objects are morphisms (of some given category) with a common codomain, and whose morphisms are commuting triangles where two morphisms of each of such triangles share the said common codomain."
      ],
      "links": [
        [
          "category theory",
          "category theory"
        ]
      ],
      "raw_glosses": [
        "(category theory) A category whose objects are morphisms (of some given category) with a common codomain, and whose morphisms are commuting triangles where two morphisms of each of such triangles share the said common codomain."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "overcategory"
    }
  ],
  "word": "slice category"
}

This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-01 from the enwiktionary dump dated 2024-04-21 using wiktextract (f4fd8c9 and c9440ce). 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.