"inverse system" meaning in English

See inverse system in All languages combined, or Wiktionary

Noun

Forms: inverse systems [plural]
Head templates: {{en-noun}} inverse system (plural inverse systems)
  1. (algebra) A set of algebraic structures (which are part of a concrete category; e.g., groups) and a set of morphisms between them (e.g., group homomorphisms) which all together form a small category which is the image of a contravariant functor whose domain is a directed poset. Wikipedia link: Inverse limit Categories (topical): Algebra Related terms: inverse limit
    Sense id: en-inverse_system-en-noun-b7K2oi53 Categories (other): English entries with incorrect language header Topics: algebra, mathematics, sciences

Inflected forms

Download JSON data for inverse system meaning in English (1.7kB)

{
  "antonyms": [
    {
      "word": "direct system"
    }
  ],
  "forms": [
    {
      "form": "inverse systems",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "inverse system (plural inverse systems)",
      "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": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A set of algebraic structures (which are part of a concrete category; e.g., groups) and a set of morphisms between them (e.g., group homomorphisms) which all together form a small category which is the image of a contravariant functor whose domain is a directed poset."
      ],
      "id": "en-inverse_system-en-noun-b7K2oi53",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "algebraic structure",
          "algebraic structure"
        ],
        [
          "concrete category",
          "concrete category"
        ],
        [
          "group homomorphism",
          "group homomorphism"
        ],
        [
          "small category",
          "small category"
        ],
        [
          "contravariant functor",
          "contravariant functor"
        ],
        [
          "directed",
          "directed"
        ],
        [
          "poset",
          "poset"
        ]
      ],
      "raw_glosses": [
        "(algebra) A set of algebraic structures (which are part of a concrete category; e.g., groups) and a set of morphisms between them (e.g., group homomorphisms) which all together form a small category which is the image of a contravariant functor whose domain is a directed poset."
      ],
      "related": [
        {
          "word": "inverse limit"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Inverse limit"
      ]
    }
  ],
  "word": "inverse system"
}
{
  "antonyms": [
    {
      "word": "direct system"
    }
  ],
  "forms": [
    {
      "form": "inverse systems",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "inverse system (plural inverse systems)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "inverse limit"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Algebra"
      ],
      "glosses": [
        "A set of algebraic structures (which are part of a concrete category; e.g., groups) and a set of morphisms between them (e.g., group homomorphisms) which all together form a small category which is the image of a contravariant functor whose domain is a directed poset."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "algebraic structure",
          "algebraic structure"
        ],
        [
          "concrete category",
          "concrete category"
        ],
        [
          "group homomorphism",
          "group homomorphism"
        ],
        [
          "small category",
          "small category"
        ],
        [
          "contravariant functor",
          "contravariant functor"
        ],
        [
          "directed",
          "directed"
        ],
        [
          "poset",
          "poset"
        ]
      ],
      "raw_glosses": [
        "(algebra) A set of algebraic structures (which are part of a concrete category; e.g., groups) and a set of morphisms between them (e.g., group homomorphisms) which all together form a small category which is the image of a contravariant functor whose domain is a directed poset."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Inverse limit"
      ]
    }
  ],
  "word": "inverse system"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-04-30 from the enwiktionary dump dated 2024-04-21 using wiktextract (210104c 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.