Further thoughts on categories and their applications. References: Toposes. Theories and Triples can be found at Michael Barr's home page, www.math.mcgill.ca/barr/. The notes suggested by Jochen, below, are a good starting point.
Applications: There are a lot of different types of categories and categorical constructions. So there are, potentially, lots of possible applications. It is probably best to have a team approach, with at least one expert in the area of the intended application and at least one expert in category theory. But all experts have to learn something of the language, basic results, concepts of both fields, then they can see if one set of ideas can map onto another. This sort of provides an answer to Nick's question. One can benefit (or perhaps enjoy) a field of abstract mathematics if the underlying concepts can be made intuitively clear with a minimum of technical complexity. Specifically can categories relate to questions of metaphor and analogy? Rosen in "Life Itself" belabors an approach to metaphor which strikes me as heavy-handed yet not comprehensive enough. Is there a better connection? --I think that's a good question. --John On 8/12/08 3:39 PM, "Jochen Fromm" <[EMAIL PROTECTED]> wrote: I wonder if category theory can be applied to model metaphors and analogies? Or perhaps gene regulatory networks? The following slides seem to be suitable for folks with a good undergrad math background: "Category Theory for Beginners" http://www.cs.toronto.edu/~sme/presentations/cat101.pdf -J. ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
