"left inverse" meaning in All languages combined

{
  "antonyms": [
    {
      "word": "right inverse"
    }
  ],
  "forms": [
    {
      "form": "left inverses",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "left inverse (plural left inverses)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "In order for a function to have a left inverse it must be injective."
        }
      ],
      "glosses": [
        "A related function that, given the output of the original function, returns the input that produced that output."
      ],
      "id": "en-left_inverse-en-noun-yL79eHO-",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "function",
          "function"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A related function that, given the output of the original function, returns the input that produced that output."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Category theory",
          "orig": "en:Category theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "27 73",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "For a given morphism f : X → Y, its right inverse (if it has one) is a morphism s : Y → X such that s∘f= mbox id_X."
      ],
      "hypernyms": [
        {
          "_dis1": "15 85",
          "word": "inverse"
        }
      ],
      "id": "en-left_inverse-en-noun-s8pIGGQE",
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "morphism",
          "morphism"
        ]
      ],
      "raw_glosses": [
        "(category theory) For a given morphism f : X → Y, its right inverse (if it has one) is a morphism s : Y → X such that s∘f= mbox id_X."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ],
      "translations": [
        {
          "_dis1": "26 74",
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "neuter"
          ],
          "word": "Linksinverses"
        }
      ]
    }
  ],
  "word": "left inverse"
}

{
  "antonyms": [
    {
      "word": "right inverse"
    }
  ],
  "categories": [
    "English countable nouns",
    "English entries with incorrect language header",
    "English lemmas",
    "English multiword terms",
    "English nouns",
    "Translation table header lacks gloss"
  ],
  "forms": [
    {
      "form": "left inverses",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "left inverse (plural left inverses)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "inverse"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "en:Mathematics"
      ],
      "examples": [
        {
          "text": "In order for a function to have a left inverse it must be injective."
        }
      ],
      "glosses": [
        "A related function that, given the output of the original function, returns the input that produced that output."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "function",
          "function"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A related function that, given the output of the original function, returns the input that produced that output."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Category theory"
      ],
      "glosses": [
        "For a given morphism f : X → Y, its right inverse (if it has one) is a morphism s : Y → X such that s∘f= mbox id_X."
      ],
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "morphism",
          "morphism"
        ]
      ],
      "raw_glosses": [
        "(category theory) For a given morphism f : X → Y, its right inverse (if it has one) is a morphism s : Y → X such that s∘f= mbox id_X."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "neuter"
      ],
      "word": "Linksinverses"
    }
  ],
  "word": "left inverse"
}