Definition:Metagraph
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Definition
A metagraph $\GG$ consists of:
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 $f$ |
This page has been identified as a candidate for refactoring of basic complexity. 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. Until this has been finished, please leave {{Refactor}} in the code.
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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.
Also known as
This page has been identified as a candidate for refactoring of medium complexity. Give these actual definitions and make them subpages in their own right Until this has been finished, please leave {{Refactor}} in the code.
New contributors: Refactoring is a task which is expected to be undertaken by experienced editors only. Because of the underlying complexity of the work needed, it is recommended that you do not embark on a refactoring task until you have become familiar with the structural nature of pages of $\mathsf{Pr} \infty \mathsf{fWiki}$.To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Refactor}} from the code. |
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.