Though the categories take their origin in the nature of the subject, they are objective and valid for objects of experience, because experience is possible alone through them.  They are not the product, but the ground of experience.  The second difficulty concerns their applicability to phenomena, which are wholly disparate.  By what means is the gulf between the categories, which are concepts and a priori, and perceptions, which are intuitous and empirical, bridged over?  The connecting link is supplied by the imagination, as the faculty which mediates between sensibility and understanding to provide a concept with its image, and consists in the intuition of time, which, in common with the categories, has an a priori character, and, in common with perceptions, an intuitive character, so that it is at once pure and sensuous.  The subsumption of phenomena or empirical intuitions under the category is effected through the Schemata[1] of the concepts of the understanding, i.e., through a priori determinations of time according to rules, which relate to time-series, time-content, time-order, and time-comprehension, and indicate whether I have to apply this or that category to a given object.

[Footnote 1:  The schema is not an empirical image, but stands midway between this (the particular intuition of a definite triangle or dog) and the unintuitable concept, as a general intuition (of a triangle or a dog in general, which holds alike for right- and oblique-angled triangles, for poodles and pugs), or as a rule for determining our intuition in accordance with a concept.]

Each category has its own schema.  The schema of quantity is number, as comprehending the successive addition of homogeneous parts.  Filled time (being in time) is the schema of reality, empty time (not-being in time) the schema of negation, and more or less filled time (the intensity of sensation, indicating the degree of reality) the schema of limitation.  Permanence in time is the sign for the application of the category of substance;[1] regular succession, for the application of the concept of cause; the coexistence of the determinations of one substance with those of another, the signal for their subsumption under the concept of reciprocity.  The schemata of possibility, actuality, and necessity, finally, are existence at any time whatever (whensoever), existence at a definite time, and existence at all times.  By such schematic syntheses the pure concept is brought near to the empirical intuition, and the way is prepared for an application of the former to the latter, or, what is the same thing, for the subsumption of the latter under the former.