[CG] Re: Higher Order Sign Relations

Cf: Higher Order Sign Relations • 4 http://inquiryintoinquiry.com/2022/08/06/higher-order-sign-relations-4/ Re: Higher Order Sign Relations • 3 https://inquiryintoinquiry.com/2019/12/23/higher-order-sign-relations-3/ Re: Cybernetics ( https://groups.google.com/g/cybcom/c/UwInmSnuv0c ) ::: Cliff Joslyn ( https://groups.google.com/g/cybcom/c/UwInmSnuv0c/m/ouaEgeo6BgAJ ) <QUOTE 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, All, Here’s a few sources I recall most vividly for the way they captured the attractions of categories, plus a few I hope to get back to someday. These come from a bibliography I assembled early in the 90s plus a number I added over the course of that decade. • Prospects for Inquiry Driven Systems ( https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems ) • Bibliography ( https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems#… ) • Arbib ( https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems#… ) • Hindley ( https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems#… ) • Lambek ( https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems#… ) • Lie ( https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems#… ) • Manes ( https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems#… ) • Smullyan ( https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems#… ) • Stoy ( https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems#… ) The following sources may also be of interest. • Mili A., Mili, F., et al. ( https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems#… ) 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 ( https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems#… ) “Categories, Allegories”, a category-theoretic approach to binary relations. Regards, Jon