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Mar 18, 2010 at 4:47 comment added Reid Barton I think I agree most with this answer. In particular, we can think of monoidal categories as $A_\infty$ monoids in categories, and it sounds like Theo has a map of $A_n$ monoids for some small $n$ (like 2 or 3, I forget the indexing). However, I have been brought up to think of things that are not even $A_\infty$ as pretty awful, so perhaps Theo should try to find some extra "twisting" kind of structure (but I feel it may not be a purely category-theoretic notion).
Mar 17, 2010 at 11:48 history answered Thomas Kragh CC BY-SA 2.5