"factor through" meaning in All languages combined

{
  "forms": [
    {
      "form": "factors through",
      "tags": [
        "present",
        "singular",
        "third-person"
      ]
    },
    {
      "form": "factoring through",
      "tags": [
        "participle",
        "present"
      ]
    },
    {
      "form": "factored through",
      "tags": [
        "participle",
        "past"
      ]
    },
    {
      "form": "factored through",
      "tags": [
        "past"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "*"
      },
      "expansion": "factor through (third-person singular simple present factors through, present participle factoring through, simple past and past participle factored through)",
      "name": "en-verb"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "verb",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English phrasal verbs with particle (through)",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Category theory",
          "orig": "en:Category theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1995, Colin McLarty, Elementary Categories, Elementary Toposes, page 142",
          "text": "LEMMA 16.3 An arrow f#x3A;A#x5C;rightarrowB is epic iff 1#x5F;B is the smallest sub-object of B that f factors through.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Said of a morphism: to be equal to a composition of two morphisms, one of which is the given morphism (that is being said to be \"factored through\")."
      ],
      "id": "en-factor_through-en-verb--s8moLTa",
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "morphism",
          "morphism"
        ],
        [
          "composition",
          "composition"
        ]
      ],
      "raw_glosses": [
        "(category theory) Said of a morphism: to be equal to a composition of two morphisms, one of which is the given morphism (that is being said to be \"factored through\")."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    }
  ],
  "word": "factor through"
}

{
  "forms": [
    {
      "form": "factors through",
      "tags": [
        "present",
        "singular",
        "third-person"
      ]
    },
    {
      "form": "factoring through",
      "tags": [
        "participle",
        "present"
      ]
    },
    {
      "form": "factored through",
      "tags": [
        "participle",
        "past"
      ]
    },
    {
      "form": "factored through",
      "tags": [
        "past"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "*"
      },
      "expansion": "factor through (third-person singular simple present factors through, present participle factoring through, simple past and past participle factored through)",
      "name": "en-verb"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "verb",
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English phrasal verbs",
        "English phrasal verbs with particle (through)",
        "English terms with quotations",
        "English verbs",
        "en:Category theory"
      ],
      "examples": [
        {
          "ref": "1995, Colin McLarty, Elementary Categories, Elementary Toposes, page 142",
          "text": "LEMMA 16.3 An arrow f#x3A;A#x5C;rightarrowB is epic iff 1#x5F;B is the smallest sub-object of B that f factors through.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Said of a morphism: to be equal to a composition of two morphisms, one of which is the given morphism (that is being said to be \"factored through\")."
      ],
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "morphism",
          "morphism"
        ],
        [
          "composition",
          "composition"
        ]
      ],
      "raw_glosses": [
        "(category theory) Said of a morphism: to be equal to a composition of two morphisms, one of which is the given morphism (that is being said to be \"factored through\")."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    }
  ],
  "word": "factor through"
}