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The definition and the annotated bibliography are given for Feynman category.
I wonder how useful this could be in related to elucidate the cohomological and motivic quantization via correspondences (Kan extensions in the setup of Feynman categories can help getting the pushforwards, Connes-Kreimer Hopf algebra, Feynman transform (which in some cases gives coefficients in the formal development of the Feynman integal, basically being partition functions, hence connection to graphs).
Not much the wiser as to what they’re for, but I added the recent
I made the definition tally with
Not much the wiser as to what they’re for,
Feynman categories are just another way of saying “colored operad”. This was proven in Batanin-Kock-Weber 15. I have now highlighted this a bit more in the entry, both in an brief Idea-section and in a Properties section (both telegraphic for the time being, just meant to point to that reference)
I see. So rather an unnecessary name.
An independent proof of the result is also claimed in section A.1 of
(This appeared as a preprint in the same month, just a little earlier. It cites Batanin et al. as “in preparation”. But then Caviglia’s article seems not to have been published(?))
So rather an unnecessary name.
Possibly. I suppose it was motivated from the previously established term Feynman transform.
… and “colored operad” is just another way of saying “symmetric multicategory”.
Usually when a concept has more than one name, we only have one page about it. Should we merge Feynman category with operad or symmetric multicategory?
I’d think the explicit definition of “Feynman category” seems sufficiently different from that of operad/multicategory to not be the same concept under a different name. The proof of their bi-equivalence seems to be rather non-trivial. (?) In this case it seems better to me to keep separate entries, albeit with clear cross-linking.
An example of where we have different pages for equivalent concepts is clone and Lawvere theory. The difference is in the presentation.
Ah, I see; the 2-categories are only biequivalent. It makes sense to keep the pages separate then.
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