From: BenSprott@gmail.com   
      
    Is anyone interested in sharing ideas on the following basic notion:   
      
   XML documents with URLs are objects   
   Hyperlinks are morphisms   
   The web has category structure   
   Groups have Topos structure   
      
      
      
   We know that the internet, defined as html objects with hyperlinks,   
   has category structure:   
      
   Understand websites as objects, and hyperlinks as morphisms   
   - hyperlinks compose in an associative manner   
   - each hyperlink has a unique source and a unique target   
   - every page naturally refers to itself and we have an identity   
      
   Starting here, we hope to build more rich structures.   
     In a usenet group, like the one we are using, we find that people   
   talk and talk.  Can we take this talk to represent, in some sense, the   
   internal language of some category.  If our group becomes very   
   cohesive, and we have linking between many of the postings, which is   
   to mean that postings are now refering to ther postings, can we   
   consider this, or model this, by a more richly structured category?  I   
   imagine that some groups can be modelled as toposes.  The question is,   
   how to do we understand the links between  postings in a group as   
   reflecting a type of categorical structure like Topos structure?   
     One place for inspiration is academic journals where the hyperlink   
   has a very old cousin, namely the reference.  The reference has a   
   semantics but that semantics is embedded in the natural language   
   sentences surrounding the reference which is turn embedded in the   
   academic article.  How can we reflect some of this in a computing   
   environment?   
      
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