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am splitting this off from Lie algebra, for ease of cross-linking.
moving a comment on Lie algebra objects by David Roberts (from here):
Urs,
please don’t take my post as evidence of ignorance, but of poorly expressing the intent of the comment. The mention of the work of Heuts was meant to be an aside, and the point was that Lurie gave a nice intro to Lie algebra objects, and I thought it might be interesting to think about your recent work looking at weight systems/braids in light of this. Also in light of the question here which someone else asked in relation to detail about the universal category with a Lie algebra object, also mentioned in Lurie’s talk. If the weight systems/braids/etc have something sensible to say about this universal case it could be interesting.
When Heuts’ work actually appears (as a talk or preprint) I will definitely add it in the appropriate place.
added example of Leibniz algebras as internal Lie algebras in the Loday-Pirashvili category.
In today’s arXiv:2103.08939 (and a series of previous articles referenced there) there is a claim of an interesting class of examples, or at least one interesting example, of internalization of Lie algebras (and then $L_\infty$-algebras) into categories of modules over certain Drinfeld deformed noncommutative algebras.
Am still trying to absorb this better.
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