Category theory embraces uniformly (but on a fairly abstract level) things like database schema’s, ontologies, programming language type systems, analogies between knowledge domains (spider silk and music have been mapped in this way) and whole branches of mathematics (not the least). In a nut, category theory is the universal language to describe and relate things with some structure. Anything graph-like can be fed to categories and functors. Including finance and law.
Categories also offer an approach to quantum computing which, much like topological quantum computing, emphasize the importance of diagrams, graphs and knots (braids). So, this section highlights categorical aspects of quantum computing and complements the topological approach.
Ologs are real-world, easy to understand examples of categories and are, next to semantic nets and RDF (triple stores, quad stores, ontologies…), knowledge representations. While the semantic world articulates software (Apache Jena, SPARQL etc.), ologs articulate abstract analogies and mathematical thinking. Database schema’s is a great example where concrete software practice meets abstract mathematics via ologs and functorial maps (between a schema and its datasets).