\begin{definition}[Definition:Metagraph]
A '''metagraph''' $\GG$ consists of:
* objects $X, Y, Z, \ldots$
* morphisms $f, g, h, \ldots$ between its objects
These are subjected to the following two axioms:
{{begin-axiom}}
{{axiom | n = 1
        | lc= ''Domains''
        | t = Every morphism $f$ has associated an object $\operatorname{dom} f$, called the '''domain''' of $f$
}}
{{axiom | n = 2
        | lc= ''Codomains''
        | t = Every morphism $f$ has associated an object $\operatorname{cod} f$, called the '''codomain''' of $f$
}}
{{end-axiom}}
{{refactor|As the following is not part of the definition but of explanatory nature only, it is to be separated out and put into its own section, and not "Note" or "Comment" or anything lame like that.}}
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.
\end{definition}