Definition:Metacategory

Definition
A metacategory is a metagraph subject to extra restrictions.

As such, a metacategory $\mathbf C$ consists of:


 * A collection $\mathbf C_0$ of objects $X, Y, Z, \ldots$
 * A collection $\mathbf C_1$ of morphisms $f, g, h, \ldots$ between its objects

The morphisms of $\mathbf C$ are subjected to:

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.

Also see

 * Category