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Also I would imagine there is some relevant prehistory here, such as Simpson’s weak units conjecture, and the analysis of this in dimension 3 by Joyal-Kock. I don’t know how this relates to the development described in the article.
added pointers to
Christoph Dorn, Associative $n$-categories, talk at 103rd Peripatetic Seminar on Sheaves and Logic (pdf)
Christoph Dorn, Associative n-categories PhD thesis (pdf)
added today’s arXiv identifier for
Despite these strictness properties, it is conjectured that every weak n-category is weakly equivalent to an associative n-category with strict units.
Isn’t this just a version of Simpson’s conjecture ? I would crosslink if I were sure in what conventionsassumption in this issue are.
@zskoda well, I think it’s related but somewhat orthogonal. Roughly:
I have adjusted the first sentences to include more adjectives and links illuminating what the concept is about:
The notion of associative $n$-categories (ANCs, Dorn 2018, Reutter & Vicary 2019) is a semi-strict algebraic model for higher category theory based on the geometric shape of globular sets with strictly associative composition: All higher coherence laws in associative $n$-categories are strict, except for weak versions of higher exchange laws.
Notably the fact that “associative $n$-categories” are modeled on globular sets was not mentioned before, nor was there a link to Globular nor homotopy.io (which I have added now).
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