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Rune Haugseng
Rune Haugseng
8:40 AM
@SaalHardali I don't think it's rude, but I haven't come across such a construction
In Lurie's model I guess you can make such an adjunction using the "categorical patterns" machinery from the appendix of HA (with the right adjoint being the pullback you mention)
Or maybe you can instead restrict the active maps in Fin_* to have fibres of size $\leq s$
(Then I think the left adjoint is just composing with the inclusion into Fin_*, so it's easy to see it's fully faithful)
 
 
1 hour later…
Rune Haugseng
Rune Haugseng
9:59 AM
With the slight drawback that that's not actually a category, since such maps aren't closed under composition...
 
 
5 hours later…
Dylan Wilson
Dylan Wilson
3:14 PM
@SaalHardali @RuneHaugseng barwick's 'operator category' story does arity truncations well (arxiv.org/pdf/1302.5756.pdf)
 
 
1 hour later…
blank_space
blank_space
4:36 PM
Some of the recent starred conversations on the right have made me reconsider whether I should attempt to engage with this chat. I was somewhat shocked at the people in what had appeared to be enviable positions who also feel vulnerable, so here's me being temporarily empowered to share my experience. For it's worth, in response to something else upthread, I'm not a woman either.

I am not a homotopy theorist, but homotopy-adjacent, and have had a longstanding interest, ever since my last year of grad school ... which my interactions with the community have gone some way toward suppressing.
12
 
 
4 hours later…
Tim Campion
Tim Campion
8:36 PM
@blank_space I have a lot of sympathy for your situation, and appreciate you putting yourself out there like this! As a grad student myself, I'm not sure what to say about the larger career aspects going on. But I would be curious to hear more about the "homotopy-adjacency" of your work. I suspect that there are a lot of people who have the sense that homotopy theory / higher category theory might be useful for their work, but are daunted by the idea that in order to learn this stuff you have to digest at least one 1000-page book before getting any real payoff. I think this is a misconcepti…
Side question: I seem to have accidentally succeeded in inputting text longer than the 600 character maximum (including duplicating some of it) -- and I think I've seen others do this before too. How does one do this on purpose?
But anyway, I really would be curious to hear about the kinds of reasons you're interested in learning this stuff for -- there's probably some way to streamline your approach to the subject by customizing it to the kinds of questions you're interested in applying it to.
 

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