8,270 reputation
11734
bio website personal.us.es/fmuro
location Seville, Spain
age
visits member for 3 years, 7 months
seen 20 hours ago

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


Aug
18
comment pontryagin dual and maps between spectra
The answer to your question is obviously yes, since any abelian group arises as the group of homotopy classes of maps between certain spectra. If you want BC-duals to show up, your abelian group is $\pi_0I_{\mathbb{Q}/\mathbb{Z}}F(A,B)$, where $F(A,B)$ is the function spectrum. If you want to use the BC-duals of $A$ and $B$, you should first try to anser your question for ordinaryt abelian groups instead of spectra.
Aug
14
answered Zigzags and contractibility of categories
Aug
13
comment Zigzags and contractibility of categories
I think Omar is right. You seem to be describing the Gabriel-Zisman localization of $\bf C$ at all arrows, i.e. the groupoidification of $\bf C$. Hence $Z\bf C$ is the fundamental groupoid of the nerve of $\bf C$, and it has an initial object iff it is trivial, but this says nothing about the higher homotopy groups of $\bf C$, unfortunately.
Aug
13
reviewed Approve suggested edit on simple explanation of simplicial volume=4g-4 when genus $\ge 1$
Aug
11
awarded  Enlightened
Aug
11
awarded  Nice Answer
Aug
7
revised Taking zeroth cohomology of a dg-module over a dg-category is “good” on representables, but probably “bad” on cones
slight correction on the hypotheses on $M$
Aug
7
comment Taking zeroth cohomology of a dg-module over a dg-category is “good” on representables, but probably “bad” on cones
Take $R$ to be a $k$-algebra...
Aug
7
answered Taking zeroth cohomology of a dg-module over a dg-category is “good” on representables, but probably “bad” on cones
Aug
7
reviewed Approve suggested edit on Is there a finitely presented group with infinite homology over $\mathbb{Q}$?
Aug
7
comment Behavior of the projective dimension of modules in a continuous chain of extensions
The projective dimension of $L$ is also $\leq n$. This result is known as Auslander's Lemma.
Aug
6
comment Reconstructing a morphism of exact triangles in the homotopy cat. of a dg-cat. using a “functorial cone map”
Of course, take $k[x]$ and $k[x]/(x)\hookrightarrow k[x]/(x^2)\twoheadrightarrow k[x]/(x)$
Aug
5
answered Reconstructing a morphism of exact triangles in the homotopy cat. of a dg-cat. using a “functorial cone map”
Aug
5
comment Reconstructing a morphism of exact triangles in the homotopy cat. of a dg-cat. using a “functorial cone map”
The answer to both questions is no in general, as you guess. Counterexamples are not that obvious though. If I have time (and can get a better connection where I am) I'll come back with one.
Aug
1
comment Why does Neeman avoid t-structures?
I dare not judge what's the main aim of Newman's triangulated book, but I'd say it's more connected to Brown repeatability. It has a basic part, but it's not a basic book.
Aug
1
comment Why does Neeman avoid t-structures?
I don't see why t-structures are a must in a triangulated category book. It's an important topic, of course, but not comparable to determinants.
Jul
31
comment Why does Neeman avoid t-structures?
you can try to explain what you think it's a misunderstanding.
Jul
31
reviewed Approve suggested edit on Quantile as solution to minimization problem
Jul
30
comment Why does Neeman avoid t-structures?
I don't think it aims at being exhaustive, he even mentions something like that at the introduction, actually it's rather the contrary, there are no examples at all! In addition, most of the book is devoted to new material.
Jul
30
reviewed Approve suggested edit on Hypersurfaces with rational self-maps