Andrea Marino
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Member for 5 years, 7 months
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Last seen this week
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Analogues of Sullivan Theory at a prime for coformality
Very nice!! Thanks. I was also wondering if such a model (as the Heuts model) somehow give an explicit way to compute the p-adic homotopy groups of spaces. In rational homotopy theory, this is quite effective. For example it has been used by Arone and Lambrechts to show the homotopy spectral sequence of knots in $\mathbb{R}^d, d \ge 4$, collapses.
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A fiber-like method to show equivalence of infinity categories
Not sure why a cofinal map should be a weak categorical equivalence. In HTT 4.1.1.3 it is proved that a cofinal map is also a weak homotopy equivalence, but not an equivalence of $\infty$-categories. What am I missing? However, that's exactly the kind of theorem I am looking for
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Homotopy fibers of infinity functors
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Left Proper model structure on the category of non-symmetric operads in chain complexes
Thank you very much Fernando! I am flattered to get an answer by you in person! Indeed, thanks to the theorem you cited, I managed to show what I wanted, in combination with some nlab proposition on base-change. That is, in the hypothesis of thm 1.11, if V has in addition cofibrant tensor unit, then the base change $\textrm{Ass}/Op(V) \to B/Op(V)$ is a Quillen equivalence for $B \to \textrm{Ass}$ being a cofibrant resolution. This is true for $V=Ch(k)$ no matter which $k$, since the unit is always cofibrant. No left-properness needed!
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Left Proper model structure on the category of non-symmetric operads in chain complexes
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Notation for spectral sequences
@Carl-FredrikNybergBrodda: not sure I got your point. Things you are citing have a fixed meaning, and I am okay with that. Thing here is that we have a whole category of spectral sequences, and just one letter to denote them. Since spectral sequences comes with three sub/super-scripts, it's not even wise to use other sub/super-scripts to distinguish them. So if I have more than one spectral sequence, I have to use a messy notation like $E^{p,q}_r(G)$ (where $G$ for example stands for Grothendieck) or ${}_1E^{p,q}_r, {}_2 E^{p,q}_r, {}_3 E^{p,q}_r$..
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Notation for spectral sequences
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Homotopy totalization and chains - reference
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Homotopy totalization and chains - reference
Thanks! The rectification result solves even other issues I had in a neighborhood of this one!
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Homotopy totalization and chains - reference
Thank you very much to both of you. Very insightful comments! I do even know the BK sseq, but I hadn't realized its convergence was essentially the failure or not of the qi above...
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Name for homotopy totalization of Goodwillie tower (in embedding calculus)
Dear @TomGoodWillie, it's an honour to receive the answer from you in this matter! :D thank you all for the suggestions, I find 'completion' to be a nice word. Maybe I would like 'profinite completion' more, because one get this from "finite-degree" approximations and then take the limit. Also, completion could be confused with group completion in case one has a $\mathbb{E}_1$ structure as it happens in knots. But profinite maybe hints at some precise meaning that does not exist. What do you think? Update: "Goodwillie -Weiss completion" probably answers to my concern, didn't see that.