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bio website personal.us.es/fmuro
location Seville, Spain
age
visits member for 3 years, 11 months
seen 9 hours ago

I'm a mathematician interested in algebraic topology, category theory, homological algebra, and K-theory.


Dec
25
comment homotopy fixed points and fixed points
Qiaochu of course, did you maybe understand anything different from my comments?
Dec
24
comment homotopy fixed points and fixed points
what I mean is that the homotopy fixed points functor is the total left derived functor of the plain fixed points functor, hence if you apply both functors to a cofibrant object you obtain weakly equivalent results, whereas you don't if you apply them to a non-cofibrant object. This is not much, really, and won't be very helpful, so I include it as a comment.
Dec
23
comment homotopy fixed points and fixed points
For 1), the answer depends on the explicit model of $THH(X)$ you take.
Dec
21
comment The definition of $SK_1$ for an arbitrary ring
I can't answer you second question, but in my opinion your proposal has a drawback: it's not a functor. In general you have a map from the group of units to K_1, and you can consider it's quotient. It just happens to be a split mono when the ring is commutative.
Dec
21
comment What's so special about $1$-categories?
for me it's strict, but regardless of conventions weak and strict 2-categories generalize to higher dimensions.
Dec
21
comment What's so special about $1$-categories?
"the alternative does not generalize to higher values of 2", what?!
Dec
17
comment equivalence in simplicial category
In simplicial categories, morphism objects are simplicial sets, so they do have vertices. For a simplicial category, $\pi_0S$ is not a discrete groupoid, it's a category.
Dec
17
comment A More Advanced Version of Aluffi's Chapter 0
Maybe it's only me, but in my expierence the notion of adjunction is even difficult to starting graduate students.
Dec
17
comment equivalence in simplicial category
An equivalence in a simplicial category $S$ is a map (i.e.~a vertex in some morphism simplicial set) which becomes an isomorphism in $\pi_0S$.
Dec
17
comment A More Advanced Version of Aluffi's Chapter 0
How can you teach elementary algebra assuming advanced algebra concepts?
Dec
15
reviewed Approve Is there a probability theory developed in intuitionistic logic?
Dec
15
reviewed Approve intuitionistic interpretation of classical logic
Dec
12
reviewed Approve Geometry of the space of circles in the Euclidean plane
Dec
12
comment Homotopical nilpotency of self homotopy equivalence
@MarkGrant sorry, I understood that the image should be nullhomotopic as a selfmap of G.
Dec
11
comment Model bicategories
Ah, sorry, I daresay 'no'.
Dec
11
comment Model bicategories
Is there any example (which is not an honest model category)?
Dec
11
comment Homotopical nilpotency of self homotopy equivalence
Because no map in aut$_1(G)$ is nullhomotopic.
Dec
11
comment Homotopical nilpotency of self homotopy equivalence
According to your definition the number on the right is infinity, so technically the answer is yes.
Dec
11
comment Uniqueness of ring structure on spectra.
@Max sorry, I'm just wondering what's your motivation to read those papers. I can imagine that somebody knowing answers to 1) and 3) may be motivated to read the papers, but I'm curious about what other motivations would be.
Dec
10
comment Uniqueness of ring structure on spectra.
Why are you reading these papers if you don't have an answer to 1) (and 3))?