Factorization

Factorization is breaking a process into steps. If getting from A to C always passes through B, then the process A → C factors through B. It decomposes into A → B followed by B → C.

In arithmetic, factoring 12 gives 2 × 2 × 3 — the number broken into pieces that multiply to rebuild it. In category theory, a morphism f: A → C factors through B when there exist morphisms g: A → B and h: B → C such that f = h ∘ g. B is the intermediate that the process must pass through.

Factorization reveals hidden structure. If every instance of a process passes through the same intermediate, that intermediate is doing real work — it is a necessary waypoint, not an accident. Click-through rate factors through impression and conversion rate because every click requires first being seen (impression) and then acting (conversion).

When this library uses factors-through as a predicate, the subject is a process and the object is an intermediate it must pass through on the way to its result.