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Tim Hosgood (Nov 06 2025 at 12:58):Does anybody have a copy of the handwritten notes for I Aitchison's "String diagrams for non-abelian cocycle conditions"? It's quite widely cited but I can't find a scan or even summary of the notes anywhere. I'm hoping that this isn't another source lost to folklore...
Kevin Carlson (Nov 06 2025 at 19:51):This might be a good thing for the CT mailing list if it doesn't show up here.
John Baez (Nov 06 2025 at 22:58):Did you try this?
The abstract says:
This reports on the fundamental objects revealed by Ross Street, which he called 'orientals'. Street's work was in part inspired by Robert's attempts to use N-category ideas to construct nets of C*-algebras in Minkowski space for applications to relativistic quantum field theory: Roberts' additional challenge was that 'no amount of staring at the low dimensional cocycle conditions would reveal the pattern for higher dimensions'. This report takes up this challenge, presenting a natural inductive construction of explicit cubical cocyle conditions, and gives three ways in which the simplicial ones can be derived from these. (A dual string-diagram version of this work, giving rise to a Pascal's triangle of diagrams for cocycle conditions, has been described elsewhere by Street). A consequence of this work is that the Yang-Baxter equation, the 'pentagon of pentagons', and higher simplex equations, are in essence different manifestations of the same underlying abstract structure. There has been recent interest in higher-categories, by computer scientists investigating concurrency theory, as well as by physicists, among others. The dual 'string' version of this paper makes clear the relationship with higher-dimensional simplex equations in physics. Much work in this area has been done since these notes were written: no attempt has been made to update the original report. However, all diagrams have been redrawn by computer, replacing all original hand-drawn pictures.
John Baez (Nov 06 2025 at 23:03):Street's paper is here and it cites "Iain Aitchison: String diagrams for non-abeIian cocycle conditions, handwritten notes, talk presented at Louvain-la-Neuve, Belgium, 1987". I bet Street still has these notes.
David Michael Roberts (Nov 06 2025 at 23:11):Maybe. He's had to move office more than once in the past decade (building chess by the university) and also more seriously retired.
John Baez (Nov 07 2025 at 07:58):I knew he was retired but not about the repeated moves.
Anyway, Tim should definitely ask on the category theory mailing list. It's a shell of its former self, but many old-timers still read it - the sort of people who are much more likely to have Aitchison's notes than us youngsters here.
David Michael Roberts (Nov 07 2025 at 12:02):I am the beneficiary of one such move, as I inherited a bunch of books!
Alexander Campbell (Nov 12 2025 at 09:19):I asked Ross about these notes today, which he had shown to me in his office some time in 2013–2014. He said that he had made a scan of them years ago which he might still have as a PDF file. Stay tuned.
Tim Hosgood (Nov 12 2025 at 14:47):amazing, thank you so much!