 Category theory, understood as a branch of pure mathematics, has frequently been described as a “general theory of mathematical structures”, e.g., by Mac Lane (1986, 1996). But what exactly is meant by “structure” here?  At least two relevant notions are mentioned in the literature. First, a structure can be understood in the set- and model-theoretic sense, i.e., as a tuple consisting of a domain and an ordered sequence of relations, functions, and distinguished elements used for the interpretation of a formal language. (This is the notion of “relational system” we appealed to above more informally.)  Such structures are often called “Bourbaki structures” in this context. Their properties are usually defined axiomatically, e.g., by the group axioms or the Dedekind-Peano axioms for arithmetic.