1,673 reputation
722
bio website math.jhu.edu/~beardsle
location Baltimore, MD
age 27
visits member for 3 years, 8 months
seen yesterday

Learning.


Aug
28
comment Why is Set, and not Rel, so ubiquitous in mathematics?
I think the main reason we stick so close to functions is purely historical. Set theory and category theory are natural generalizations of things that already existed - that is, geometry, space and time, as was said above. However, I'd also say that there seems to be a general theme of looking at relation-eqsue objects when one starts working with motives. That is, subsets of $X\times Y$ satisfying some property, rather than functions $X\to Y$.
Aug
24
comment Can formal logic give a precise notion of “canonical”?
I am not a logician, but I agree with @DavidCorwin here. It's clear that there are lots of logical ways to pick one shoe over the other, but that seems to be missing the point. It's like working with objects versus pointed objects. However, this seems like a tacitly illogical state of affairs, in that by asking to pick one "over" the other, you're assigning value in some way, which seems a little non-mathematical.
Aug
24
answered Higher Degree Data in a Cosimplicial Quasicategory and Delooping
Aug
23
revised Higher Degree Data in a Cosimplicial Quasicategory and Delooping
added 248 characters in body
Aug
22
asked Higher Degree Data in a Cosimplicial Quasicategory and Delooping
Aug
14
awarded  Nice Question
Jul
23
comment Detection of stable homotopy by K-theory spectra
@BenWieland Sorry, so in saying that char. 0 fields and transcendental char. p fields detect everything, you're saying that they detect elements of all heights? Or are you saying rather that the detect the entire image of J?
Jul
23
accepted Detection of stable homotopy by K-theory spectra
Jul
23
comment Detection of stable homotopy by K-theory spectra
Wow Ben, thank you so much for your answer! That's really helpful. So, it would seem then that from a chromatic point of view, algebraic K-theory is (at least morally) sort of stuck at height 1?
Jul
22
asked Detection of stable homotopy by K-theory spectra
Jul
12
comment Multiplicative Structures on Moore Spectra
For what it's worth, it seems like what you're getting at is this fundamental difficulty we have in spectra of talking about "modding out by ideals," since you're only looking at localization versus taking quotients.
Jul
2
awarded  Inquisitive
Jul
2
awarded  Curious
Jun
21
revised Topological quotient Hopf-algebras and “change-of-rings”
added more information to the question
Jun
20
comment forcing and set theory
It might help to check out the FAQ and spend a little more time writing your question. Explain why you're interested, what's the motivation? Describe previous work on the topic, etc.
Jun
20
asked Topological quotient Hopf-algebras and “change-of-rings”
May
30
comment Thom Spectra and Hopf-Galois Extensions of Ring Spectra
I should also mention that that convergence I mention definitely holds for a LOT of interesting Thom spectra: $MU$, $MSO$, $MSU$, $X(n)$, Baker and Richter's $M\xi$. And the alternate situation (being an extension of the 2-adic sphere spectrum) holds for $MO$.
May
30
comment Thom Spectra and Hopf-Galois Extensions of Ring Spectra
Ah thanks @JustinNoel I had seen that word (primitives) used in some places. Perhaps it will be less confusing if I start using that rather than cofixed points.
May
30
revised Thom Spectra and Hopf-Galois Extensions of Ring Spectra
edited tags
May
30
asked Thom Spectra and Hopf-Galois Extensions of Ring Spectra