Towards arrow-theoretic semantics of ontologies: conceptories

Ontologies [1] are used in computer science for representing and sharing knowledge about the real world. Usually ontological structures are described in terms of classes(of things) and relationships(between things). This is rather similar to category-theoretic notions of objects and morphisms (see [2, 3] for information about the algebraic category theory). Since the category theory already brings us many benefits in other areasofcomputer science, it is desirable to find arrowtheoretic approaches in the area of knowledge representation. 1 Some authors proposed category-theoretic techniques helpful in different aspects of knowledge representation[5, 6]. Usually they operate with (co)limits that are convenient for merging and interoperating between existing models and metamodels. Our aim is to find a category-theoretic tools that would be useful for description of ontological models from the very beginning.