Timeline for Is the normalized simplicial bar construction of an operad a cooperad?
Current License: CC BY-SA 4.0
5 events
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| Jul 24, 2022 at 16:20 | comment | added | Eugene Rabinovich | Proposition 9.29 just restates the theorem of Fresse; I couldn't find mention of additional structure on the normalized chains. If I understand the Ginzburg-Kapranov paper correctly, they only introduce the cooperad (or its dual operad) which I called B(P). | |
| Jul 24, 2022 at 16:18 | comment | added | Eugene Rabinovich | Thanks for the references. If I understand correctly, Ching constructs a topological cooperad (the topological analogue of B(P)) and shows that the geometric realization of the simplicial object I mention in the original post coincides with this topological symmetric sequence. But I couldn't tell whether he shows that there is a dg-cooperad structure on the chains N(P), which I think would amount to showing that the cooperad structure map on the topological cooperad takes simplices to smash products of simplices. | |
| Jul 23, 2022 at 18:15 | history | edited | Nicholas Kuhn | CC BY-SA 4.0 |
added 209 characters in body
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| Jul 23, 2022 at 16:09 | comment | added | Connor Malin | It is Proposition 9.29 for anyone looking, though he actually cites Fresse's "Koszul duality of operads and homology of partition posets" | |
| Jul 23, 2022 at 3:43 | history | answered | Nicholas Kuhn | CC BY-SA 4.0 |