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bio website personal.us.es/fmuro
location Seville, Spain
age
visits member for 4 years, 4 months
seen 8 hours ago

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


1d
reviewed Approve Solving a system of linear inequalities — what is the dimension of the solution set?
2d
comment Homotopy pullback preserving functor
Denis thanks, now I understand Edoardo's and Adeel's concern. I agree with Edoardo that I wouldn't be able to prove the claim without asking that the functor preserves pull backs.
2d
comment Homotopy pullback preserving functor
@AdeelKhan if it preserves fibrations and weak equivalences, then it preserves homotopy fiber sequences.
2d
comment Homotopy pullback preserving functor
Concerning the first claim, I don't see any problem, a square is a homotopy pull-back iff the induced map between homotopy fibers of parallel arrows is a weak equivalence.
May
22
comment Higher-dimensional category theory on objects
One of the points of category theory, ordinary and higher, is concentrating everything on morphisms. You can replace abelian groups with sausages, as long as you use the same morphisms you end up with the same category.
May
22
comment is there a moduli of stable infinity categories?
You would need good geometric properties to settle the infinitesimal part. As far as I know, this is rather open. I know some advances are being made with respect to deformations.
May
22
comment Different ways of having infinite global dimension
Thanks for your comments. I also think this is maybe a difficult question. Strange examples are... strange.
May
22
comment Model structure on non-negative differential graded algebras with homological grading
Sorry, I think I misunderstood your notation. In any case, I don't think you can make it easier than in the comments since the bounded case isn't more complicated than the unbounded case, that you assume.
May
22
comment Different ways of having infinite global dimension
Sorry, your argument convinced me at a first glance, but I don't see the contradiction. There might be a sequence of cyclic modules with finite but divergent projective dimension.
May
22
comment Model structure on non-negative differential graded algebras with homological grading
$iL_{\text{bounded}}$ is not the restriction of $L_{\text{unbounded}}$. In the bounded case, you don't ask fibrations to be surjective in degree $0$. Actually, it wouldn't work if you did. The inclusion is a left Quillen functor, not a right Quillen functor (although it is a right adjoint). The model structure on bounded complexes is not transferred from unbounded complexes.
May
21
comment is there a moduli of stable infinity categories?
Rathen than answering, I'm interested in what you know :) What is a connected triangulated dg-category and where can I find references about their moduli stack?
May
21
comment Different ways of having infinite global dimension
@BenjaminSteinberg thanks, I just didn't come up with the idea of using that f.g. modules are 'compact' w.r.t. direct sums.
May
21
comment Different ways of having infinite global dimension
@BenjaminSteinberg yes, the projective dimension can be computed on cyclic modules, but I don't see why this answers negatively my question. What am I missing?
May
21
revised Different ways of having infinite global dimension
title improved
May
21
asked Different ways of having infinite global dimension
May
21
comment Inverse limit in shape theory
You're then talkin about the completeness of a certain category rathen than theory.
May
21
comment Model structure on non-negative differential graded algebras with homological grading
Non-negative chain complexes over an arbitrary ground commutative ring form a symmetric monoidal model category satisfying the monoid axiom with the structure you indicate, hence the first part of your question has a positive answer by Schwede-Shipley. As for your second question, I think the answer may be positive too, I know it is for nonsymmetric operads at least, see Spitzweck's old preprint for the general case.
May
21
comment Inverse limit in shape theory
What does 'complete' mean here?
May
19
reviewed Approve Transcendence of products of certain real algebraic numbers
May
19
revised A generalization of the Spanier-Whitehead construction
One typo and uniformization of notation