Definition:Metacategory

Definition
A metacategory $\mathcal C$ consists simply of:
 * objects $X, Y, Z, \ldots$
 * morphisms (or arrows or maps) $f, g, h, \ldots$

A metacategory 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.