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Matteo Capucci (he/him) (Apr 30 2026 at 10:15):Does anyone have access to the paper:
Goguen, Joseph. "Categorical foundations for general systems theory." Advances in cybernetics and systems research 1 (1973).
Jacob S. Zelko (Apr 30 2026 at 17:20):This sounds quite like a fascinating paper @Matteo Capucci (he/him) -- have you had any luck finding it? I actually spent 15/20 minutes trying to track it down and apparently I do not think it has been digitized. However, I found that it seems to be present in a copy of the "Advances in cybernetics and systems research: Proceedings of the European Meeting, Vienna, 1972" which just so happens to be down the street from me at the MIT Library here in Cambridge!
Jacob S. Zelko (Apr 30 2026 at 17:20):At this point, I am quite curious about this paper and have read some of Goguen's work in the past so would be interested in reading it myself further. Have you had any luck finding the paper Matteo?
V Slicer (Apr 30 2026 at 17:45):I haven't been able to find it either when I was looking earlier, this paper discusses it though, it deals with how Goguen emphasized that 'colimits are how to compose systems.'
Matteo Capucci (he/him) (Apr 30 2026 at 19:19):No I haven't that's why I asked here. I don't know even what's in it, but I'm intrigued by the title!
Matteo Capucci (he/him) (Apr 30 2026 at 19:20):V Slicer said:
I haven't been able to find it either when I was looking earlier, this paper discusses it though, it deals with how Goguen emphasized that 'colimits are how to compose systems.'
this seems to be citing a different paper, though I wouldn't be surprised if the gist is the same
Jacob S. Zelko (Apr 30 2026 at 20:14):Matteo Capucci (he/him) said:
No I haven't that's why I asked here. I don't know even what's in it, but I'm intrigued by the title!
Alright, well, then it is settled! I think I shall make this a mini-quest to see if I can find this from the library.
Matteo Capucci (he/him) (May 03 2026 at 11:20):That's be wonderful @Jacob S. Zelko thanks a lot :D
Jacob S. Zelko (May 06 2026 at 13:23):Just a little update here @Matteo Capucci (he/him) : with the help of a friend, we tracked it down in the off-site library archives. We put in a scan request yesterday and should have a scanned copy back by May 27th if not sooner!
Matteo Capucci (he/him) (May 19 2026 at 13:25):Hello, someone (not @Jacob S. Zelko) sent me a scan of the paper, which I found very interesting. However, it's not possible for me to share it. So I digitised it and put it here: https://github.com/mattecapu/goguen-categorical-foundations
Happy reading! It's a pretty visionary paper.
Jacob S. Zelko (May 19 2026 at 19:25):Oh great @Matteo Capucci (he/him) ! Glad you were able to acquire a copy!
I started taking a look at this copy too so far and it's always interesting to see Goguen's perspective. I remember reading his A Categorical Manifesto a year or so ago and found it interesting in his scope of vision.
Jacob S. Zelko (May 19 2026 at 19:26):This paper is pretty interesting as well so far -- the ambition is there. I am on the second page currently and am puttering away with his notion of what he is calling "T-objects". Have you finished it yet Matteo?
Joe Moeller (May 19 2026 at 21:44):Last sentence of the paper: "Contemplate ."
Matteo Capucci (he/him) (May 20 2026 at 06:22):I can hear the angelic choir
Matteo Capucci (he/him) (May 20 2026 at 06:23):Jacob S. Zelko said:
Have you finished it yet Matteo?
Yes! I had to read it to copyedit it anyway
Matteo Capucci (he/him) (May 20 2026 at 06:23):a T-object ends up to just he a copresheaf over a category of 'time intervals'
Matteo Capucci (he/him) (May 20 2026 at 06:24):Then he claims these objects interconnect by gluing (colimits) and you can get their behaviour by variable sharing (limits)
Matteo Capucci (he/him) (May 20 2026 at 06:29):The first anticipated by a few decades the idea of composition as colimits which afaik was reintroduced only by Fong and Baez in 2015
The second afaik is only ever pondered again by Schultz, Spivak and Vasilakopolou in 2016 (although to much greater depth and focusing on the temporality aspect)
In particular the idea that behaviour composes by limit has become a central aspect of DOTS, and now we can cite an eminent precedent! Before we could only gesture at Willems (who understood behavioural systems are very important) and Adam (who wrote his thesis about formalizing Willems with CT).
V Slicer (May 20 2026 at 14:37):Thanks for copyediting and sharing Matteo Capucci (he/him)!
Matteo Capucci (he/him) said:
In particular the idea that behaviour composes by limit has become a central aspect of DOTS, and now we can cite an eminent precedent!
Goguen was already articulating aspects of entering the DOTS yoga? That's very much a tradition we're a part of 
V Slicer (May 20 2026 at 14:41):It's always interesting to come across others in the past exploring these same ideas, recently I encountered some cases where I believe assume-guarantee reasoning might have been anticipated, or differently articulated.
Todd Trimble (May 21 2026 at 12:05):What does DOTS stand for?
V Slicer (May 21 2026 at 12:21):DOTS stands for Double Operadic Theory of Systems:
Double Operadic Theory of Systems (DOTS), neé (Doubly) Categorical Systems Theory ((D)CST), is a formal mathematical theory of systems. A theory of systems is the algebra of a double operad: the operations of the operad describe how to compose systems, while the algebra substantiates these operations into actual functors between categories of systems. This structure combines both the compositional and structural aspects of systems theory, with the operad part describing compositionality and the categorical part describing the structure of systems.
John Baez (May 21 2026 at 17:58):It's David Jaz Myers' way of working with decorated/structured cospans, lenses and other open systems in a unified framework, @Todd Trimble. The ARIA project on safeguarded AI was going to use it, but I'm not sure if that's still true. There's been a change of leadership.
Todd Trimble (May 21 2026 at 18:29):I'm sorry that I didn't know this.
David Corfield (May 22 2026 at 13:22):DOTS is still steaming ahead. Occasionally we even see some T(riple)OTS.
V Slicer (May 22 2026 at 13:23):My excuses if my answer at the time was brief @Todd Trimble, I was in the middle of writing a longer comment about DOTS in this stream, where Matteo shared another paper using DOTS in that stream, but I forgot to link back to it. Thank you for adding that John.
V Slicer (May 22 2026 at 13:31):David Corfield said:
DOTS is still steaming ahead. Occasionally we even see some T(riple)OTS.
Where might one learn more about TOTS? What more is it accounting for over DOTS?
David Corfield (May 22 2026 at 16:01):For an explicit appearance of triple categories in categorical systems theory, try @Matteo Capucci (he/him)'s talk Constructing triple categories of cybernetic processes, or more directly, try slides 70-72 of his slides.
John Baez (May 23 2026 at 07:21):Someday people will joke that only tots use TOTS. Today is not that day. But I thought I would defuse the tension.