Definition:Metagraph
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domain, codomain
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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:
\((1)\) $:$ Domains Every morphism $f$ has associated an object $\operatorname{dom} f$, called the domain of $f$
\((2)\) $:$ Codomains Every morphism $f$ has associated an object $\operatorname{cod} f$, called the codomain of $f$
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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.
Give these actual definitions and make them subpages in their own right
The objects of a metagraph are also called vertices or nodes.
The morphisms of a metagraph are also called edges or arrows.
The domain of a morphism is also called its origin or source.
The codomain of a morphism is also called its destination or target.
Definition:Graph (Category Theory)
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Definitions/Category Theory
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