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3:24 AM
@SaalHardali I think I've only seen this discussed for one-colored operads, in @GijsHeuts's Goodwillie approximations to higher categories, section 4.1.
 
 
1 hour later…
4:29 AM
Thanks for your posts. They're both better than I'd hoped. I'd anticipated recrimination or silence.

I've heard it asserted that one can pick pieces of the edifice and learn to apply them independently, given enough faith, and I've attempted this independently a few times, in addition to trying the sequential, foundations-first approach (with some difficulty—I knew only the definition and a few first examples of simplicial sets). The difficulty with this approach for me is that without familiarity with the underpinnings, it can be hard to be confident one is applying a result correctly. It
 
 
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7:43 AM
Meta-question: Every once in a while I have a question specifically about a paper, that could probably best/only be answered by its author(s). When I know that (a subset of) these authors are on this chat, I am conflicted about whether I should write (one of) the authors directly or post my question here, possibly with a ping.
I personally gravitate towards the latter, as these questions may be of general interest, but on the other hand sending an email would be the traditional approach, and also some authors might find it unpleasant to have their work dissected in such a public forum. What are your thoughts on this? I would be particularly interested in hearing from said authors.
 
8:26 AM
@AdrianClough In my case, I'm happy to receive questions here, and will answer here if I can do so in just a few words, but for a longer answer I prefer to respond via email. I suppose if the question is to point out an error, I would prefer to receive that privately ;)
 
@AlexanderCampbell Ok, thanks!
 
 
2 hours later…
10:10 AM
Hi, anyone knows a reference of an infinity categorical construction of the cup product in relative cohomology? something in the spirit of, if F is a sheaf of rings in D(Z) on X, the functor A--> F(X;A) promotes to a lax symmetric monoidal functor Open(X)-->Mod(F(X)), where the source is with respect to the union symmetric monoidal structure.
 
 
4 hours later…
2:12 PM
@OmarAntolín-Camarena @RuneHaugseng @TimCampion Thanks for the help!
 
 
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4:19 PM
@blank_space For what is worth, I am sure that I look like very plugged into the homotopy theory community (and by any objective standard I am), but the feeling of not being really "a part" of it never really goes away. I don't know if I have ever been one to appear dismissive to your question, but if so I apologize. I do believe we are on the whole a very welcoming community but there's no denying there are some rough edges [...].
 
@blank_space wow. thank you so much for this. it was very raw. i hear you, and i want good things for you. most of all, i wish you a sense of peace.
 
I don't believe "you suck" (that's basically never true, especially so if you've survived so long in academia -- beware of the impostor syndrome), and my wish is that you would feel free to ask questions and chat about math with any of us without fear of judgement. God knows I asked plenty of stupid questions here
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first and foremost, please know that i for one do truly want your opinion, and i'm grateful that you were willing to share it.
[haha i see me and denis are responding simultaneously -- i love it]
i don't think i have any answers for you; i don't know if anyone does (nor was that necessarily the point of your message). but i will share what your messages brought up for me. on the other hand, if you think there is some way i could be helpful to you, or if you would like to continue discussing these sorts of issues with me privately, please do feel free to reach out by email -- from an anonymous account, if you like.
i have also felt largely rejected by the homotopy theory community. allowing myself to say that "out loud", i feel embarrassed, and forced to recognize how much privilege i have had through the years.
i say that, nevertheless, partly because i want to point out that a sense of rejection seems practically built-in to academia. it may be my own projection, but it seems to me that all but the "blessed few" are dealing with it constantly. but perhaps more likely is that everyone feels this way, even those who may seem blessed from a distance.
relatedly (and i think i also said this when i shared a bunch of feelings a while back), i find it really unfortunate and discouraging how little the mathematics community tends to "respond" to research: at best you give a few talks, at worst it's like it never happened at all. this makes it so that the default experience is to feel like you are "falling through the cracks". perhaps more than anything else, this is something that i would like to change about the culture of mathematics.
i also really relate to the pain of trying to be/become someone who you are not. it feels so awful. i have gone down the rabbit hole "i will finally be cool if only i know some [insert field of math here]" so, so, so many times. and every single time, at the bottom of it i am always forced to reckon with my own shortcomings.
back in grad school, i tried to force myself to read through a textbook on rep theory, because i was sure that i would finally be cool if only i knew some rep theory. this was driven almost entirely by a sense of shame, inadequacy, and self-hatred. it was a really bad time.
6
and all of a sudden, i understood what it was like for most non-math people trying to learn math, when they say that it makes no sense "because" it's abstract and irrelevant. i think what is actually going on is that we who love math learn it out of joy and excitement, and any other motivation to learn it makes it painful.
it sounds like you are already aware of this phenomenon, but i think it's worth emphasizing: with any deeper mathematics (say beyond an undergrad course), i have never been able to truly internalize anything that i didn't "need".
i've found this to be particularly true with HTT and HA. there is just so much there, and so much of it is so technical. i've had quite a few experiences where some bit of one of those books was totally impenetrable, up until all of a sudden it was exactly what i "needed" and then it felt like lurie had read my future self's mind when he wrote it.
i'm really sorry to hear that your interactions with the homotopy theory community have been so negative (the subvocalized "obviously", etc.). i'm also sad to realize that i'm not surprised, and ashamed to recognize that i have certainly contributed to this. speaking for myself, i think this comes from a desperation to seem like i belong to the in-crowd. this is not an excuse, just an observation.
in any case, i hope deeply that we in this chatroom can take this as a reminder to be welcoming and gentle with newcomers.
@AdrianClough this is a good question! as i've expressed previously, i would be thrilled to see more dialog in here based on our own research. this goes towards the lack of "response" that i just mentioned above. my understanding is that some might see it as good form to message all the coauthors of a work when you have a question; but personally i would consider that a lower priority.
of course, i would imagine that everyone agrees with @AlexanderCampbell, in that they would rather have an error pointed out privately instead of publicly!
 
 
2 hours later…
6:09 PM
@AaronMazel-Gee Right! I had also occurred to me that asking on here rather than by email would help increase the visibility people's research.
 

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