factor through

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").

Verb

  1. 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").
    • 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:

Forms

factors through factoring through factored through