bio | website | math.jhu.edu/~beardsle |
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location | Baltimore, MD | |
age | 27 | |
visits | member for | 3 years, 8 months |
seen | yesterday | |
stats | profile views | 2,143 |
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 |