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Ben Steffan
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Mathematics
Associated with Math.SE; for both general discussion & math qu...
5
23
Ben Steffan
01:32
Is it just "you take the functors in the other direction obtained from Cartesian straightening and then unravel the definitions to show that these are adjoint?"
Ben Steffan
01:20
@Thorgott I'm intrigued. How do you get that the objects of the subcategory are left adjoints?
Ben Steffan
yst 23:05
but at the same time I do not envy you over the end-of-thesis stress
Ben Steffan
yst 23:05
I believe in you :)
Ben Steffan
yst 23:00
that's not a lot :/
Ben Steffan
yst 23:00
oh, ok
Ben Steffan
yst 22:59
how much time do you have left on the thesis?
Ben Steffan
yst 22:57
I guess that makes sense
Ben Steffan
yst 22:57
huh
Ben Steffan
yst 22:54
bordism is so strange
Ben Steffan
yst 22:53
but $(\infty, \infty)$-categories??
Ben Steffan
yst 22:53
ah, what else
Ben Steffan
yst 22:49
@Thorgott that sounds... very scary
Ben Steffan
yst 22:49
:o
Ben Steffan
yst 22:43
what's your thesis' topic?
Ben Steffan
yst 22:43
not that that necessarily means much but
Ben Steffan
yst 22:43
relative to me at least you seem to understand a lot :)
Ben Steffan
yst 22:35
this is just absurd
Ben Steffan
yst 22:35
I do not understand how people do $\infty$-category theory at the research level
Ben Steffan
yst 22:34
yeah :'(
Ben Steffan
yst 22:31
I thought it was this one but apparently not
Ben Steffan
yst 22:31
Moser-Rasekh-Rovelli
Ben Steffan
yst 22:31
...this is the exact paper I pulled up lol
Ben Steffan
yst 22:29
apparently there's a paper out there that does it this way, for $(\infty, n)$-categories
Ben Steffan
yst 22:29
the model independent proof is still a lot of work
Ben Steffan
yst 22:20
more precisely, apparently if you could produce the yoneda embedding in some other way, then you could have a nicer proof
Ben Steffan
yst 22:19
oh, on that note: I learned today that apparently you can proof straightening/unstraightening model-independently if you already know it for anima
Ben Steffan
yst 22:14
happens to the best of us
Ben Steffan
yst 22:14
That's alright, that's alright :)
Ben Steffan
yst 22:13
but in the end the thing they were asking about is just strange, independent of that
Ben Steffan
yst 22:12
If they had a solid understanding of the concept of $\infty$ then the discussion would probably have been somewhat shorter
Ben Steffan
yst 22:05
That's why this discussion came about in the first place
Ben Steffan
yst 22:05
And maple
has
some concept of infinity like that, and allows you to operate on it, apparently?
Ben Steffan
yst 22:04
@GroveRover But this is coming from maple?
Ben Steffan
yst 22:03
@XanderHenderson what kind of show? standup comedy?
Ben Steffan
yst 22:02
it has been 0 days since wheel theory has been mentioned in this chatroom
Ben Steffan
yst 22:02
ducks
Ben Steffan
yst 22:01
to some extent.
Ben Steffan
yst 22:01
@GroveRover I literally just told you you can.
Ben Steffan
yst 21:59
...
Ben Steffan
yst 21:58
I'm telling you that it is not. Look up, say, the extended real line.
Ben Steffan
yst 21:57
As for extending operations to it, things like $c \cdot \infty = \infty$ when $c > 0$ are fairly benign and commonplace
Ben Steffan
yst 21:56
It
does
exist in formal mathematics, even if it is not an element of the real line.
Ben Steffan
yst 21:21
sure, but why are you telling me this
Ben Steffan
yst 21:19
whether this is the intended semantics in maple or not is impossible to say for an outsider
Ben Steffan
yst 21:18
again, I find positing $5 = 0 \cdot \infty$ bizarre, but it is a definition I could technically make
Ben Steffan
yst 21:17
there's no generally agreed upon meaning of the expression $0 \cdot \infty$, so asking whether it equals some value is not a mathematical question
Ben Steffan
yst 21:16
as I pointed out above, this question is not well-posed
Ben Steffan
yst 21:13
I'm sure there's some kind of maple forum where you could ask, no?
Ben Steffan
yst 21:12
I have no idea whether it is a bug