factor through
In real, traceable use. Part of the curated seed collection; community review is coming.
Meaning · English
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").
Where it’s used:
Used
American English
Examples
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.
Usage example from English Wiktionary (CC BY-SA 4.0, retrieved 2026-07-30)
Sources & notes
Adapted from English Wiktionary (CC BY-SA 4.0, retrieved 2026-07-30 via kaikki.org).
Common questions
What does “factor through” mean?
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").
Is “factor through” formal or informal?
No register label has been reviewed yet — treat it as neutral and check the usage notes above.