The categories are the attribution of a predicate to a subject. They are specifically supreme classes of every possible predicate, with which it is possible to order the whole reality.
For Aristotle, the categories are groups or primary genres which collect all the properties that may be the explanation of ‘being’. They are the predicaments of ‘being’, which refer to primary qualities (the immutable essences of objects), or secondary (the mishaps that may change).
The categories of Aristotle have an objective value, because they refer to concrete entities. Our judgments use them not only according to a relationship purely logical, typical of syllogism, but assembling them owing to the intuitive capacity to effectively grasp the relationship between the real objects. But beyond that, to each of the categories it relates a part of those semantic constructs of the discourse that have to do with the real world: for example, a name or a noun refers to the category of substance; the adjectives to quality, those indefinite to quantity, or to the relationship etc. It is therefore assumed that for Aristotle categories are a classification of the components which make a discourse.
Starting from the distinction between the objective level and the semantic one, that was not missed in Aristotle, who, however, would not know what to attribute to one and what to the other, Immanuel Kant admits that to judge, source of all objective discourse, is a 'multifaceted activity, which arises from the application of different categories or pure concepts, through which the intellect unifies multiple data from sensitive intuition.
These concepts, however, are transcendental, namely that they need starting data in order to activate, without which they would be empty: it's because of the sense organs that an object is "given," to us becoming a phenomenon; with categories then it is "thought".
Then, unlike Aristotle, for whom categories belonged to the ontological reality of ‘being’, the Kantian categories fit in to the intellect; that is, they become the ‘a priori’ functions, or means of working of our thought that frame reality according to its own preconceived scheme. They do not apply to reality in itself, but only to the phenomenon.
As in Aristotle the categories needed judgment to be used, then in Kant they require a supreme activity, of a thought in the process of being created, to exercise their unifying function of the manifold. The categories are the multiple facets of a prism which is called thought; they are unifying acts, but not yet active, only potentially activated.
This opens the question of the deduction of the categories, that is, how to justify the use we make of them: for example, is it legitimate to assign different categories to the same object?
This is the problem faced by Kant in the Transcendental Deduction of Critique of Pure Reason, to unify categories, finding a principle from which they can all derive. This principle will be found in the ‘I think’ or transcendental apperception.
Kant will be accused of having locked himself up in a subjectivism with no way out, given that his categories do not serve to know the reality as it is in itself, but only as it appears to us.
With Fichte they assume a different role: while Kant had intended to unify the multiple, for Fichte they assume the inverse aim of multiplying the uniqueness of the ‘I’, bringing it to divide and produce unconsciously the ‘non-I’. Thus the categories of the intellect have also a real or ontological value, albeit unconscious. The ‘thinking’ is to create, but only at the level of intellectual intuition.
In Hegel, instead, it is the same logic that becomes creative. The cognitive categories of Kant, which were merely "formal", become together "form and content": they are logical-ontological categories, determinations of the Idea as it proceeds dialectically. An object exists to the extent that it is rational, that is, only if it falls within a logical category.
For Nietzsche, finally, categories become the result of the evolution of the breed: their effectiveness would be given not by the ability to reflect what is true, but by the utility in aiding survival. Concepts taken and endorsed by ethological-philosophical studies of Konrad Lorenz, who defined the categories the 'apparatus image of the world. "