Kant

An image is an empirical product of either sensibility or reproductive imagination, while a schema is the determination of the formal aspect of the manifold with respect to a priori concepts. The schema can therefore never be empirical; it is pure.
             The deduction is setting out to prove the possibility of the categories as a priori modes of knowledge. In proving this, Kant must naturally show how the categories can relate to intuition. For, if the categories are a priori concepts and they do not receive empirical input from the intuition, then one of two things is possible. Either (1) Kant is either claiming that the totality of experience is a priori and therefore he is creating another idealistic philosophy, or (2) experience itself is impossible. Thus, as Kant would have neither the former proposition nor the latter, he must explain, in the deduction, how the pure concepts relate to intuition. The schematism, as the first section in the Analytic of Principles, restates the need of a "third thing" or a method of presenting the categories to intuition so that they may apply to experience. However, Kant goes on to state the exact time determinations, made possible by the imagination, of the categories. Thus, Kant does not just leave the reader with the potentiality or necessity of the categories to apply to intuitions, as is outlined in the deduction; he, in the schematism, shows us how the categories actually apply to intuitions by revealing their actual time determinations or the schemata themselves.
             Kant needs to show how the categories, as the a priori concepts of the understanding, can subsume empirical intuitions under them and thus relate to experience. In this, there seems to be a large problem; namely, how can a priori concepts be applied to empirical intuitions? As all things empirical are necessarily a posteriori, there is a division between them and the faculty of judgment, which possesses concepts a priori.