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Ari Rosenfield (she/her) (Apr 08 2025 at 20:43):I've been wondering recently about the historical context around this paper by Borceux-Quinteiro, which maybe someone here can shed light on.
Specifically, I wonder what, if anything, the authors intended to do with the results of that paper. The introduction was not very illuminating as to their intent, and the paper contains exactly one example, namely enrichment over abelian groups, which case had entire algebra textbooks dedicated to it long before the paper came out (I'm thinking of Bo Stenstrom's Rings of Quotients). As far as I can tell from a search on mathscinet, it hasn't been cited very much, and the authors didn't write a followup paper or anything (again, not one that is easy for me to find).
On the rare occasion where I talk to fellow category theorists about this paper, the general vibe seems to be either "yeah, the community seems to have forgotten about that paper for some reason," or that people feel like their definition of an enriched site is somehow not correct or useful? Anyway, I'm just trying to learn anything I can about it.