Representation of the Metagraph from the Position of the Theory of Categories

The article proposes the concept of category theory for describing metagraphs. In particular, a metavertex is considered as a category built on the generating set of a metagraph. This approach made it possible to consider vertices and metavertices as objects, and relations between them as morphisms. In this case, the metavertex is not a hyperedge, but a subset of the generating set, i.e., an object, along with the elements of the generating set, which does not contradict graph theory. Metavertices are a generalization of the corresponding objects of the generating set and carry a certain informational (semantic) load. At the same time, objects from the generating set can also be a generalization of some metavertices. The concepts of a static and dynamic metagraph are introduced, as well as matrix representations of a static metagraph. A static metagraph is defined by a category based on the generating set and the set of morphisms (arcs, edges) defined on the generating set, as well as the set of metavertices and the set of morphisms (metaarcs, metaedges) defined on the union of the set of metavertices and the generating set. The semantics of vertices, metavertices, arcs and metaarcs is determined by their attributes.