Fernando Muro
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Registered User
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14h |
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Homology of the dg-nerve vs Hochschild homology of the dg-category @yasha, I have no objection, I had just a question, so far unanswered. |
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14h |
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How do I find abelian subcategories of periodic triangulated categories? @Sasha, that's not true, there are degenerate $t$-structures with non-zero heart. Try with the derived category of the product of two rings. BTW, what you say at the end of your previous comment is in the line of what I think, $t$-structures are not that helpful in the general setting of the question. |
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18h |
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How do I find abelian subcategories of periodic triangulated categories? @Vivek, I don't quite understand the question in your comment above. Nevertheless, as you probably know, derived categories of abelian categories are very special among triangulated categories and $t$-structures are more relevant for them than for general triangulated categories. My comment on top is just a reflect of my perception that, unless you're working with a very special kind of triangulated categories, $t$-structures may not be so helpful. |
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22h |
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How do I find abelian subcategories of periodic triangulated categories? @Sasha, the heart of any t-structure is an abelian category, even if the t-structure is degenerate. |
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1d |
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Why are the left exact functors from an abelian category to abelian groups cocomplete and have a injective generator? OK, $\mathcal C$ is an abelian category, but what's this relevant for? I think this question is very poorly stated, and I also think that a proof of this fact can be quickly found in the standard literature on the topic. |
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1d |
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How do I find abelian subcategories of periodic triangulated categories? @Leonid, I still think they are. As you show, periodict triangulated categories only have t-structures with trivial heart, but non-periodic ones need not be better in general, that's why I say 'as good as'. |
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1d |
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Homotopy left-exactness of a left derived functor I doubt you're going to find sufficient conditions which are weak enough to apply in your general context because it is unstable. |
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2d |
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What does a singular simplex with real coefficient mean The definition of the singular chain complex is far from research level. |
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2d |
answered | Why every complex of injectives is homotopically injective (provided that, the injective dimension is finite)? |
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May 20 |
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How do I find abelian subcategories of periodic triangulated categories? t-structures are as good for periodic triangulated categories as for non-periodic ones. In my opinion not very good. |
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May 19 |
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decomposition of the injective hull of a torsion free module You can always take $I$ to be a singleton. |
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May 16 |
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Homology of the dg-nerve vs Hochschild homology of the dg-category @yasha what's Hochschild homology of a dg-category with coefficients in $\mathbb Z$? |
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May 14 |
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Homology of the dg-nerve vs Hochschild homology of the dg-category Have you at least thought whether the coefficients for both homologies could be the same kind of object? |
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May 11 |
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Why is $Lex(\mathcal{A},\mathcal{Ab})$ abelian? Does $Lex(\mathcal{A},\mathcal{Ab})\rightarrow Func(\mathcal{A},\mathcal{Ab})$ admit a left-adjoint? It would be helpful that you explained the notation you're using. |
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May 10 |
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What is a good reference (preferably thorough) for the Derived Category of a scheme/orbifold/stack? @Simon, I apologize in advance if my suggestion is innapropriate, but if you're not familiar with derived categories I would first go for derived categories of rings, then for derived categories of Grothendieck abelian categories, and finally I'd consider the particular cases you're interested in. |
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May 9 |
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Diagram spectra and Algebraic Geometry @David, if you like it, why don't you accept it? |
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May 8 |
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Diagram spectra and Algebraic Geometry @Geoffrey let me insist that you look at Morel's and Voevodsky's work. |
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May 8 |
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Homotopy classes of maps Detecting homotopic maps by means of homotopy groups is a very complicated task. There are even conjectures on it, look up 'Freyd generating hypothesis'. |
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May 8 |
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Diagram spectra and Algebraic Geometry I'd start with Morel-Voevodsky's $\mathbb A^1$-homotopy theory. |
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May 7 |
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“Cohomology at the infinity”: what does one call it I think this is called 'cohomology of ends'. It is used by Geoghegan in 'Topological Methods in Group Theory', see 3.8 (numbering of the preprint version). I first learned about this somewhere else, but I don't remember the title of the book, nor the author. |
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May 6 |
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Non-simple and non-unital rings with trivial centres ... I forgot to say that $R$ and $S$ should be non-trivial. |
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May 6 |
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Non-simple and non-unital rings with trivial centres If $R$ and $S$ are centerless then $R\times S$ is centerless and it is not simple. |
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May 5 |
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Group extensions with a non-commutative kernel Group extensions are classified by outer actions of the cokernel on the kernel together with third and second cohomology groups. All this is in an old paper by MacLane |
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May 5 |
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The use of $Ext^{1}_A(M, N)$. Yes, $M$ is projective iff that Ext vanishes for all $N$, but this question is too elementary for a research forum, I believe. |
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May 5 |
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Localization of a pure-injective module is pure-injective? I think that your definition of puré injective is not correct. Your conditions are equivalent to pure injectivity for $N$, not for $M$. |
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May 3 |
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Explicit Lie May structure on cosimplicial DG Lie algebras Why doesn't the proof answer your question? |
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May 3 |
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Split and pure exact sequence of sheaves A short exact sequence of modules is pure iff it is a filtered colimit of split ones. |
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May 3 |
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Is this square a push-out square? Yes, indeed, corrected. |
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May 3 |
revised |
Is this square a push-out square? edited body |
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May 3 |
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Split and pure exact sequence of sheaves Isn't it obvious from the definitions? |
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May 3 |
answered | Is this square a push-out square? |
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May 1 |
revised |
example re torsionless quotients of abelian groups deleted 40 characters in body |
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May 1 |
answered | example re torsionless quotients of abelian groups |
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May 1 |
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Does every simplicial polytope have a topology-preserving contractible edge? It seems that in your first paragraph you don't really talk about general simplicial complexes but only about triangulations of manifolds. |
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Apr 30 |
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“Motivic structure on higher homotopy of non-nilpotent spaces” ? In case this helps: mypage.iu.edu/~patelde |
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Apr 11 |
accepted | Commutativity of Tor |
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Apr 10 |
accepted | Homotopy excision and homotopy pushout |
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Apr 10 |
answered | Homotopy excision and homotopy pushout |
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Apr 9 |
revised |
Commutativity of Tor a typo |
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Apr 9 |
answered | Commutativity of Tor |
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Mar 28 |
revised |
A statement for a subset generated a triangulated category added 178 characters in body |
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Mar 28 |
answered | A statement for a subset generated a triangulated category |
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Mar 21 |
answered | Categorical description of the second K-group |
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Mar 10 |
revised |
Do the solutions of the Maurer--Cartan equation form a simplicial set? I've corrected the spelling of my name. |
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Mar 8 |
asked | Bases of open sets with connected intersections |
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Mar 8 |
asked | Constants sheaves on an open subset |
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Mar 3 |
awarded | ● Enlightened |
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Mar 3 |
awarded | ● Nice Answer |
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Mar 2 |
accepted | Morphisms between $K_0$ |
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Mar 2 |
revised |
Morphisms between $K_0$ added 327 characters in body |
