bio  website  personal.us.es/fmuro 

location  Seville, Spain  
age  
visits  member for  4 years, 4 months 
seen  8 hours ago  
stats  profile views  5,749 
I'm a mathematician interested in algebraic topology, category theory, homological algebra, and Ktheory.
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 pullback iff the induced map between homotopy fibers of parallel arrows is a weak equivalence. 
May 22 
comment 
Higherdimensional 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 nonnegative 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 nonnegative 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 
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is there a moduli of stable infinity categories?
Rathen than answering, I'm interested in what you know :) What is a connected triangulated dgcategory and where can I find references about their moduli stack? 
May 21 
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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 nonnegative differential graded algebras with homological grading
Nonnegative 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 SchwedeShipley. 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 SpanierWhitehead construction
One typo and uniformization of notation 