"homological algebra" meaning in All languages combined

{
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "homological algebra (uncountable)",
      "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": "Entries with translation boxes",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with German translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Italian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "The notion of chain complex is central to homological algebra.",
          "type": "example"
        },
        {
          "text": "The development of homological algebra was closely intertwined with the emergence of category theory.",
          "type": "example"
        },
        {
          "ref": "2002, C. R. Leedham-Green, S. McKay, The Structure of Groups of Prime Power Order, Oxford University Press, page 171:",
          "text": "Homological algebra for our purposes consists of studying certain abelian groups Hⁿ(G,A) and H#x5F;n(G,A), known as the nth cohomology and homology groups of the group G with coefficients in the G-module A.",
          "type": "quote"
        },
        {
          "ref": "2007, Ralph Krömer, Tool and Object: A History and Philosophy of Category Theory, Springer (Birkhäuser), page 93:",
          "text": "A similar shift of interpretation of CT took place at about the same time in another context, namely homological algebra.",
          "type": "quote"
        },
        {
          "ref": "2014, Anant R. Shastri, Basic Algebraic Topology, Taylor & Francis (CRC Press / Chapman & Hall), page 169:",
          "text": "In Section 4.1, we shall introduce some minimal amount of homological algebra needed to launch singular homology.",
          "type": "quote"
        }
      ],
      "glosses": [
        "The branch of mathematics dealing with homology and in particular with homological functors and the algebraic structures they entail."
      ],
      "id": "en-homological_algebra-en-noun-MSp1IYjb",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "mathematics",
          "mathematics"
        ],
        [
          "homology",
          "homology"
        ],
        [
          "functor",
          "functor"
        ]
      ],
      "raw_glosses": [
        "(algebra) The branch of mathematics dealing with homology and in particular with homological functors and the algebraic structures they entail."
      ],
      "related": [
        {
          "word": "homological invariant"
        }
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "de",
          "lang": "German",
          "sense": "branch of algebra",
          "tags": [
            "feminine"
          ],
          "word": "homologische Algebra"
        },
        {
          "code": "it",
          "lang": "Italian",
          "sense": "branch of algebra",
          "tags": [
            "feminine"
          ],
          "word": "algebra omologica"
        }
      ],
      "wikipedia": [
        "homological algebra"
      ]
    }
  ],
  "word": "homological algebra"
}

{
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "homological algebra (uncountable)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "homological invariant"
    }
  ],
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "English terms with usage examples",
        "English uncountable nouns",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Quotation templates to be cleaned",
        "Terms with German translations",
        "Terms with Italian translations",
        "en:Algebra"
      ],
      "examples": [
        {
          "text": "The notion of chain complex is central to homological algebra.",
          "type": "example"
        },
        {
          "text": "The development of homological algebra was closely intertwined with the emergence of category theory.",
          "type": "example"
        },
        {
          "ref": "2002, C. R. Leedham-Green, S. McKay, The Structure of Groups of Prime Power Order, Oxford University Press, page 171:",
          "text": "Homological algebra for our purposes consists of studying certain abelian groups Hⁿ(G,A) and H#x5F;n(G,A), known as the nth cohomology and homology groups of the group G with coefficients in the G-module A.",
          "type": "quote"
        },
        {
          "ref": "2007, Ralph Krömer, Tool and Object: A History and Philosophy of Category Theory, Springer (Birkhäuser), page 93:",
          "text": "A similar shift of interpretation of CT took place at about the same time in another context, namely homological algebra.",
          "type": "quote"
        },
        {
          "ref": "2014, Anant R. Shastri, Basic Algebraic Topology, Taylor & Francis (CRC Press / Chapman & Hall), page 169:",
          "text": "In Section 4.1, we shall introduce some minimal amount of homological algebra needed to launch singular homology.",
          "type": "quote"
        }
      ],
      "glosses": [
        "The branch of mathematics dealing with homology and in particular with homological functors and the algebraic structures they entail."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "mathematics",
          "mathematics"
        ],
        [
          "homology",
          "homology"
        ],
        [
          "functor",
          "functor"
        ]
      ],
      "raw_glosses": [
        "(algebra) The branch of mathematics dealing with homology and in particular with homological functors and the algebraic structures they entail."
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "homological algebra"
      ]
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "branch of algebra",
      "tags": [
        "feminine"
      ],
      "word": "homologische Algebra"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "branch of algebra",
      "tags": [
        "feminine"
      ],
      "word": "algebra omologica"
    }
  ],
  "word": "homological algebra"
}