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Jul 7, 2022 at 15:03 comment added Jonathan Beardsley Also the Koszul duals of augmented monoids and descent corings.
Jul 7, 2022 at 14:15 comment added Eric Peterson They’re fairly common: every suspension spectrum gives a comonoid, and a lesser known theorem of Bousfield says that in the K(n)-local category every spectrum admits such a structure. The “Thom diagonal” is an adjacent concept, presenting a Thom spectrum as a cotorsor for the comonoid associated to the suspension spectrum of the base space. I don’t know whether there’s an out-and-out classification available.
Jul 7, 2022 at 11:53 history edited Tintin CC BY-SA 4.0
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Jul 7, 2022 at 11:52 comment added Tintin Yes, I mean Voevodsky's stable homotopy category in the $\mathbb{A}^1$-homotopy setting
Jul 7, 2022 at 11:28 comment added Denis Nardin By "algebraic" SH, do you mean the stable motivic category?
Jul 7, 2022 at 10:11 history asked Tintin CC BY-SA 4.0