factor through

verb

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").

Ask AI about this wordChatGPTClaudePerplexityGoogle AIGrok

Meanings

verbfactor through (third-person singular simple present factors through, present participle factoring through, simple past and past participle factored through)

present singular third person factors through · participle present factoring through · participle past factored through · past factored through

  1. category theorySaid 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").

    LEMMA 16.3 An arrow f#58;A#92;rightarrowB is epic iff 1#95;B is the smallest sub-object of B that f factors through.

    1995, Colin McLarty, Elementary Categories, Elementary Toposes, page 142
Cite this entry
APA

factor through. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/factor%20through

MLA

“factor through.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/factor%20through. Accessed November 2, 2026.

Chicago

WatkinsX Dictionary, s.v. “factor through,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/factor%20through.

Source: factor through on Wiktionary, CC BY-SA 4.0.