Hyperlink
In MediaWiki, hyperlink is often denoted with [[<page name>]]. In general, hyperlink is simply a tuple, pairing a source data element and a target data element into a single structured data component. This creates a directed relation between two data elements or two names. Usually one may see the following data element examples: (where URL stands for Universal Resource Locator)
(Source, Target) (URL string of a page, A web page)
Example:
(http://localhost/index.php/Main_Page, Main Page)
This example shows http://localhost/index.php/Main_Page as the URL, or source, where the Main Page of this present MediaWiki, can be accessed by some data transmission and page rendering mechanism to deliver a human readable information. This directed relationship implemented as a World Wide Web hyperlink mechanism had profoundly changed the entire civilization since 1995. However, its developmental history could be traced back much earlier than 1995.
Hyperlink is a powerful idea originally created by pioneers, such as Ted Nelson. To learn more about Hyperlinks, the following content maybe relevant for curious minds.
A Video Clip on the inspiration of Hyperlink
To learn more about HyperText, Ted Nelson has a short clip on the movie, Lo and Behold. In this short video, Nelson presented a succinct, yet poetic way to describe Hyperlinks as streams of water particles as Ted Nelson envisioned in his early childhood, may be an evidence to show that the idea of hyperlink is fundamental, and can be grasped or taught to people at an early age.
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The Mathematics of Links
A concrete example about linguistic sentence parsing in Category Theory can be seen here:
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Hyperlinks as Sheaves
To think of hyperlink as a kind of computable data structure, the best approximation can be thought of as sheaves, or streams of water particles flowing in some related topological structure. The notion of sheaves can be referred to Category Theory, which provides an arrow chasing reasoning mechanism to perform rigorous manipulation of links.
The following video provides an interesting explanation of how to enumerate hyperlinks as binary products.
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Hyperlink and Category Theory
Hyperlink and transclusion are two concepts that are closely related to pushout nad pullback in Category Theory.