In the study of category theory, along with the usual concept of category met. As a result of developing a link between two different definitions of a category and a more general notion of an objectless category, it was found out that a whole class of isomorphic categories with objects corresponds to it. A universal mathematical apparatus of the algebra of predicates was proposed, and more precisely its central fragment, which refers to the description of logical spaces – logical analysis. As a result, the interpretation of the category in terms of the algebra of predicates was found – the predicate category Pred, and for both cases: the category with objects and the objectless category.
