Categorical criterion for the existence of universal C*-algebras

The talk is devoted to the categories introduced by T.A. Loring in the framework of an axiomatic approach to universal C*-algebras. These categories are called C*-relations. Those C*-relations that have initial objects are said to be compact. The universal C*-algebra for a compact C*-relation is defined as its initial object. It is shown that every compact C*-relation is both complete and cocomplete. As an application of the completeness of compact C*-relations, we obtain a criterion for the existence of universal C*-algebras.