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1:48 AM
Is there a reference for the following infinity category fact? I have been scouring HTT and the Barwick school papers. @DenisNardin?

If F:C\to Cat is a functor, then the associated cocartesian fibration is also a cartesian fibration if and only if F(f) has a right adjoint for all morphisms f.
 
 
4 hours later…
5:41 AM
@JohnBerman i don't know of a reference, but i think this is straightforward -- maybe the main input is that a locally cartesian fibration is a cartesian fibration iff it's so over [2]-points
i guess plus also knowing that the association from a left adjoint to its right adjoint is instantiated by cocartesian unstraightening followed by cartesian straightening
but anyways, i'd be okay with it if i saw that asserted in a paper without proof
 
6:19 AM
@JoeBerner As most people in this room know, I make a prodigious number of mistakes (though usually still being more or less correct about what I'm saying... usually...). I have done both things, that is, try to make small fixes, and basically completely restarted papers, and sometimes things in between. I think it really depends on how central the mistakes are to the paper, and perhaps more importantly, how "modular" your paper is.
By modular I basically mean is (1) your paper written like a story that would really suffer from just having stuff chopped up and shuffled aroud? or (2) is your paper like a bunch of pieces that, while having some logical dependencies, are more or less narratively independent? If it's the former, than lots of mistakes can lead to lots of dead ends in the narrative, which can really screw the paper up.
I guess it also depends on how you think. I tend to think narratively, so when something gets screwed up, I really kind of prefer to just obliterate everything and start over (not the proofs of course, or at least, the correct proofs, but all the other stuff).
 
 
3 hours later…
9:27 AM
@JohnBerman That's Corollary 5.2.2.5
 
 
3 hours later…
12:13 PM
I've read that the first Goodwillie derivative of THH is the suspension of TAQ (this is motivation for me to understand Goodwillie calculus better); does anyone know a reference that discusses this?
 
 
3 hours later…
3:18 PM
thanks for the input. I think I will fix up rather than start anew. The major statements are correct (I think!), but some of the proofs are just wrong, and some are just subtly wrong. Some of the terminology I am using is wrong, and I understand it significantly better now and can see the slight 'errors' in my definitions.
also I'm a god-awful writer, I think I got a 14% on the essay portion of general GRE, maybe I can make some readability improvements. Luckily no one has read this thing (lol)
 
 
1 hour later…
4:24 PM
I guess the tags mentioned in the recent Dan Petersen's post - namely decomposition-theorem and perverse-sheaves - are close to interests of users of this room. The proposal is to remove (decomposition-theorem), since (perverse-sheaves) seems to be sufficient.
 

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