4:33 PM
I've been trying to figure out exactly where the mistake in Ittay Weiss's construction of the BV tensor product on Dendroidal sets was.
The fact that it fails to be associative appears to come down to something subtle in Brian Day's thesis. maths.mq.edu.au/~street/DayPhD.pdf
Lemma 3.1.1 states that when we look at biclosed monoidal functors on the functor category [A,V], these are exactly in bijection with promonoidal structures on A, or more to the point, biclosed monoidal structures on [A,Set] correspond exactly to pro-monoidal structures on A in the case where the enrichment is just in sets
One direction of the bijection (the 'trace' direction) seems to only use the fact that A c F is a full dense subcategory, F is cotensored in V (Sets), and the monoidal structure on F is biclosed
But since Weiss's construction fails to give a biclosed monoidal structure on Psh(Ω), it must be the case that the trace of the BV tensor product of symmetric colored operads back to Ω is not a pro-monoidal structure
4:53 PM
5:10 PM
I copied it into an e-mail, but if anybody else is familiar with the whole BV tensor product mistake that led to all of those errata, I'm all ears
Also, if anyone wants, this question is basically the same question but with all of the context stripped out: mathoverflow.net/questions/287598/…
3 hours later…
8:39 PM
Is there any reference for the structure of $BPL$ and the motivic Adams-Novikov 2-term when working $p$-complete at an odd prime $p$? Namely, I'd like to know that $(BP_{\bullet}, BP_{\bullet} BP) \otimes \mathbb{Z} [\tau] \simeq (BPL_{\bullet, \bullet}, BPL_{\bullet, \bullet} BPL)$ and hence the motivic Adams-Novikov for the cofibre $C \tau$ of $\tau$ collapses.
2 hours later…
11:01 PM
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