Re: Higher Order Sign Relations • Discussion 2
Re: Relations, Types, Functions
Re: Cybernetics • Cliff Joslyn

CJ:

Categorical approaches to systems theory have been very attractive to me for a long time.  My current work is categorically adjacent, and I’m funding some efforts in this direction.  The category of binary relations is central to our immediate work in hypergraphs and high-order networks, but is also to any general systems theoretical approach.  I’ve approached topoi and closed Cartesian categories a few times, but admit it’s challenging.  I need something at the level that David Spivak and crew have been developing to become more fluent, if you’re aware of his work.  Any worked examples you could provide would be very useful and welcome.

Dear Cliff,

There are a few sources I recall most vividly for the way they capture the attractions of categories.  The following references come from a bibliography I collected in the early 90s plus a number I added over the course of that decade.

• Prospects for Inquiry Driven Systems • Bibliography
• Arbib
• Hindley
• Lambek
• Lie
• Manes
• Smullyan
• Stoy

The following sources may also be of interest.

• Mili • Program construction and semantics from a relational point of view, using Tarski’s approach to binary relations (Fatma Mili taught a course on this at OU).
• Freyd and Scedrov • Categories, Allegories, a category-theoretic take on binary relations.

cc: Conceptual Graphs • Cybernetics • Laws of Form • Ontolog Forum
cc: FB | Inquiry Driven Systems • Structural Modeling • Systems Science