factor through

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

1. (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").
   • 1995, Colin McLarty, Elementary Categories, Elementary Toposes, page 142:

     LEMMA 16.3 An arrow ${\displaystyle f:A\rightarrow B}$ is epic iff ${\displaystyle 1_{B}}$ is the smallest sub-object of ${\displaystyle B}$ that ${\displaystyle f}$ factors through.