bio | website | personal.us.es/fmuro |
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location | Seville, Spain | |
age | ||
visits | member for | 3 years, 7 months |
seen | 20 hours ago | |
stats | profile views | 5,010 |
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 |
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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 |
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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 |