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bio website math.jhu.edu/~beardsle
location Baltimore, MD
age 28
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Learning.


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awarded  Nice Question
18h
comment “Higher” Tangent spaces in char-p geometry - definition?
Sorry, I also don't feel like I really understand the question, but so-called Hasse-Schmidt derivations give a rather natural extension of something that plays the role of the tangent space. These also have a sensible relationship to jet spaces, which can be thought of as higher "tangent spaces" in a sense. See here arxiv.org/pdf/math/0407113.pdf
Jul
19
comment Quasicategorical Construction of a Cosimplicial Map of Rognes
Oh, and it is precisely a shearing map, I'm just trying to build it "coherently" in some sense.
Jul
19
comment Quasicategorical Construction of a Cosimplicial Map of Rognes
Au contraire @DylanWilson I think both of those comments might be immensely useful. Thanks!
Jul
19
revised Quasicategorical Construction of a Cosimplicial Map of Rognes
added 101 characters in body
Jul
18
reviewed Approve formal group laws of Abelian varieties in positive characteristic
Jul
18
asked Quasicategorical Construction of a Cosimplicial Map of Rognes
Jun
22
accepted $\Omega X$-action on spectral $X$-bundles
Jun
22
comment Lurie's Endomorphism Space vs. Endomorphisms
But yeah, I'm not being complicated at all with the algebra structure on the internal hom object, I'm truly just working through your first paragraph. I guess the point is that I should do it all with universal properties, in this case the universal property of $X^X$.
Jun
22
accepted Lurie's Endomorphism Space vs. Endomorphisms
Jun
22
comment Lurie's Endomorphism Space vs. Endomorphisms
In other words, an arbitrary map $M\to M$ is not necessarily an algebra action of $1_C$ on $M$ (obviously). So, ok. I guess that settles it.
Jun
22
comment Lurie's Endomorphism Space vs. Endomorphisms
I think maybe I don't really understand the nature of $C[X]$. I guess I was thinking the objects of $C[X]$ were the data $(C, C\otimes X\to X)$ AND a bunch of higher coherence data. But I guess that that higher coherence data is only put in when you consider algebras of this category.
Jun
22
revised Lurie's Endomorphism Space vs. Endomorphisms
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Jun
22
comment Lurie's Endomorphism Space vs. Endomorphisms
In fact, since an $A$-module is given by a map $N(\Delta)^{op}\times \Delta^1\to Top$, I suspect that the relevant map of algebras is precisely the adjoint $N(\Delta)^{op}\to Map(\Delta^1,Top)$ which picks out the map from $A$ to $End(M)$ as algebras.
Jun
22
revised Lurie's Endomorphism Space vs. Endomorphisms
added 102 characters in body
Jun
22
comment Lurie's Endomorphism Space vs. Endomorphisms
It may also be fruitful to think about the map $A\times M \to M$ as being part of a simplicial object that Lurie refers to as a "left action object." I'm trying to fiddle with that right now.
Jun
21
comment Lurie's Endomorphism Space vs. Endomorphisms
@TheoJohnson-Freyd yes you definitely also need that data. I'm not really mentioning it. I mean, quasicategorically you need a LOT of data (all the higher associativity morphisms), so it'd be nice to get that somehow without specifying an infinite list of $n$-morphisms
Jun
21
revised Lurie's Endomorphism Space vs. Endomorphisms
added 266 characters in body
Jun
21
asked Lurie's Endomorphism Space vs. Endomorphisms
Jun
17
revised $\Omega X$-action on spectral $X$-bundles
added 21 characters in body