A couple of years ago I finished a 2 to 3 year effort looking at how to use the Semantic Web for applications such as earth science modeling. This is all open-sourced R&D work and worth a look if anybody is interested in the flavor of what David Spivak wants to accomplish. As I inferred on the blog comments, to apply category theory as he intends, one might want to at least take some baby steps on how to work the ontologies with respect to what is currently available (the RDF as Nad mentioned, and SPARQL queries as Jim inferred -- good to have this knowledge on the forum ! ).

Here is my white paper in the topic:

_Knowledge-Based Environmental Context Modeling_

> Abstract:
This paper describes a semantic web architecture based on patterns and logical archetypal bulding-
blocks well suited for a comprehensive environmental modeling framework. The patterns span a
range of features that cover specific land, atmospheric and aquatic domains intended for terrestrial and
amphibious vehicles. The modeling engine contained within the server relied on knowledge-
based inferencing capable of supporting formal terminology (through the SWEET ontology and a domain specific
language) and levels of abstraction via integrated reasoning modules.

Here is the PDF:
http://entroplet.com/ref/foundation/D-knowledge_based_enviromental_modeling.pdf

if that doesn't work, I also have a version on an Amazon cloud server:

http://23.23.137.157/ref/foundation/D-knowledge_based_enviromental_modeling.pdf

I am of course interested in the category theory approach but I don't want to see the semantic web approach ignored for creating a knowledge network, as that has plenty of payoff as it now stands. If there is a core of people on the Forum with at least some expertise, as I gather from Nad and Jim's comments, we could actually get a prototype running and operational.

BTW, if you haven't guessed, I am maintaining a semantic web server here on a local machine, http://entroplet.com, and one on an Amazon cloud server http://23.23.137.157