"exact sequence" meaning in English

{
  "forms": [
    {
      "form": "exact sequences",
      "tags": [
        "plural"
      ]
    }
  ],
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      "expansion": "exact sequence (plural exact sequences)",
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  "lang_code": "en",
  "pos": "noun",
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          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
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            "Formal sciences",
            "Sciences",
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        }
      ],
      "derived": [
        {
          "word": "long exact sequence"
        },
        {
          "word": "short exact sequence"
        }
      ],
      "glosses": [
        "A sequence of modules (or groups, vector spaces, etc.; most generally, objects of an abelian category) with adjacent objects connected by homomorphisms (generally, morphisms) such that the image of one homomorphism is the kernel of the next."
      ],
      "hypernyms": [
        {
          "word": "chain complex"
        }
      ],
      "id": "en-exact_sequence-en-noun-PkKRzvQg",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "sequence",
          "sequence"
        ],
        [
          "module",
          "module"
        ],
        [
          "group",
          "group"
        ],
        [
          "vector space",
          "vector space"
        ],
        [
          "object",
          "object"
        ],
        [
          "abelian category",
          "abelian category"
        ],
        [
          "homomorphism",
          "homomorphism"
        ],
        [
          "morphism",
          "morphism"
        ],
        [
          "image",
          "image"
        ],
        [
          "kernel",
          "kernel"
        ]
      ],
      "raw_glosses": [
        "(algebra) A sequence of modules (or groups, vector spaces, etc.; most generally, objects of an abelian category) with adjacent objects connected by homomorphisms (generally, morphisms) such that the image of one homomorphism is the kernel of the next."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "exact sequence"
      ]
    }
  ],
  "word": "exact sequence"
}

{
  "derived": [
    {
      "word": "long exact sequence"
    },
    {
      "word": "short exact sequence"
    }
  ],
  "forms": [
    {
      "form": "exact sequences",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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  "hypernyms": [
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      "word": "chain complex"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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      "glosses": [
        "A sequence of modules (or groups, vector spaces, etc.; most generally, objects of an abelian category) with adjacent objects connected by homomorphisms (generally, morphisms) such that the image of one homomorphism is the kernel of the next."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "sequence",
          "sequence"
        ],
        [
          "module",
          "module"
        ],
        [
          "group",
          "group"
        ],
        [
          "vector space",
          "vector space"
        ],
        [
          "object",
          "object"
        ],
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          "abelian category",
          "abelian category"
        ],
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          "homomorphism",
          "homomorphism"
        ],
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          "morphism",
          "morphism"
        ],
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          "image",
          "image"
        ],
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          "kernel",
          "kernel"
        ]
      ],
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        "(algebra) A sequence of modules (or groups, vector spaces, etc.; most generally, objects of an abelian category) with adjacent objects connected by homomorphisms (generally, morphisms) such that the image of one homomorphism is the kernel of the next."
      ],
      "topics": [
        "algebra",
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      ],
      "wikipedia": [
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  "word": "exact sequence"
}