"direct system" meaning in All languages combined

See direct system on Wiktionary

Noun [English]

Forms: direct systems [plural]
Head templates: {{en-noun}} direct system (plural direct systems)
  1. (algebra) A set of algebraic structures (which are part of a concrete category; e.g., modules) and a set of morphisms between them (e.g., module homomorphisms) which all together form a small category which is the image of a covariant functor whose domain is a directed poset. Wikipedia link: direct system Categories (topical): Algebra
    Sense id: en-direct_system-en-noun-QVCe-F6e Categories (other): English entries with incorrect language header Topics: algebra, mathematics, sciences

Inflected forms

Download JSON data for direct system meaning in All languages combined (1.6kB)

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  "antonyms": [
    {
      "word": "inverse system"
    }
  ],
  "forms": [
    {
      "form": "direct systems",
      "tags": [
        "plural"
      ]
    }
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      "expansion": "direct system (plural direct systems)",
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  "lang_code": "en",
  "pos": "noun",
  "senses": [
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          "kind": "other",
          "name": "English entries with incorrect language header",
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            "Fundamental"
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      ],
      "glosses": [
        "A set of algebraic structures (which are part of a concrete category; e.g., modules) and a set of morphisms between them (e.g., module homomorphisms) which all together form a small category which is the image of a covariant functor whose domain is a directed poset."
      ],
      "id": "en-direct_system-en-noun-QVCe-F6e",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "algebraic structure",
          "algebraic structure"
        ],
        [
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          "concrete category"
        ],
        [
          "module homomorphism",
          "module homomorphism"
        ],
        [
          "small category",
          "small category"
        ],
        [
          "covariant functor",
          "covariant functor"
        ],
        [
          "directed",
          "directed"
        ],
        [
          "poset",
          "poset"
        ]
      ],
      "raw_glosses": [
        "(algebra) A set of algebraic structures (which are part of a concrete category; e.g., modules) and a set of morphisms between them (e.g., module homomorphisms) which all together form a small category which is the image of a covariant functor whose domain is a directed poset."
      ],
      "topics": [
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        "mathematics",
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      ],
      "wikipedia": [
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    }
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  "word": "direct system"
}
{
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    {
      "word": "inverse system"
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  "forms": [
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      "tags": [
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  "senses": [
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        "English entries with incorrect language header",
        "English lemmas",
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        "English nouns",
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      ],
      "glosses": [
        "A set of algebraic structures (which are part of a concrete category; e.g., modules) and a set of morphisms between them (e.g., module homomorphisms) which all together form a small category which is the image of a covariant functor whose domain is a directed poset."
      ],
      "links": [
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        ],
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        ],
        [
          "module homomorphism",
          "module homomorphism"
        ],
        [
          "small category",
          "small category"
        ],
        [
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          "covariant functor"
        ],
        [
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        ],
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        ]
      ],
      "raw_glosses": [
        "(algebra) A set of algebraic structures (which are part of a concrete category; e.g., modules) and a set of morphisms between them (e.g., module homomorphisms) which all together form a small category which is the image of a covariant functor whose domain is a directed poset."
      ],
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      ],
      "wikipedia": [
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  "word": "direct system"
}

This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-20 from the enwiktionary dump dated 2024-05-02 using wiktextract (1d5a7d1 and 304864d). 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.