@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

but anyways, i'd be okay with it if i saw that asserted in a paper without proof

@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).

@JohnBerman That's Corollary 5.2.2.5

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?

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)

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.