Definition:Metagraph

Definition
In particular a metagraph $\mathcal G$ consists of:
 * objects $X, Y, Z, \ldots$
 * morphisms (or arrows or maps) $f, g, h, \ldots$

A metagraph is purely axiomatic, and does not use set theory.

For example, the objects are not "elements of the set of objects", because these axioms are (without further interpretation) unfounded in set theory.