Ilias A.
  • Member for 9 years, 11 months
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solid commutative ring spectra
4 votes

Here is an example of such pair $T$ and $R$. $k$ is a finite field. $G$ is the Lie group $SO(2)$ and $G^{\delta}$ the same group but with dicrete topology. $R$ is the group algebra $k[G^{\delta}]$. $...

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Is dgCat a category or a 2-category?
11 votes

Adeel answer is perfect, I will be more basic. There is many notions of "2-category" structure here around. 1) the category of small dg-categories $\mathbf{dgCat}$ is symmetric monoidal closed ...

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Seifert--van Kampen for the loop space dga
Accepted answer
5 votes

Sketch of proof. I will use the following ingredients 0) the category of spaces will be the category of simplicial sets. All the computation are in the derived sense. 1) use the Quillen adjunction $...

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Is the "inverse" (i.e., the "cohomological") numeration for singular (i.e., $H\mathbb{Z}$-)homology of spectra "acceptable"?
2 votes

Let start with notations: $Y$ is a spectra, $H\mathbb{Z}$ is the Eilenberg-Mac Lane spectra associated to $\mathbb{Z}$ The singular homology of $Y$ is given by $H_{i}(Y)=\pi_{i}^{stable}(Y\wedge H\...

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When is the quotient by an $n$-fold loop space an $m$-fold loop space?
7 votes

May be I going to say something obvious, but I hope it will give some clarification since I feel (Maybe I'm wrong) that there is some confusion about where you are taking the homotopy cofiber ...

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bar construction and loop space cohomology
14 votes

May be I misunderstood your question. $C^{\ast}(X)$ is an $E_{\infty}$-algebra. For pointed simply connected space $X$ there is an equivalent of $E_{\infty}$-algebra between $BC^{\ast}(X)$ and $C^{\...

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Why do the model structures on dg-algebras and on dg-categories are not compatible?
7 votes

I will try to give a example in topology and then in dg-world. Suppose that $G$ and $H$ are topological groups. There is a fiber sequence $$Map_{\ast}(BG,BH)\rightarrow Map(BG,BH)\rightarrow BH$$ ...

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Zigzags and contractibility of categories
6 votes

First of all Muro's answer is perfect. This a long comment which I hope it will be helpful, it is more about intuition. I think Rezk's answer Group completion theorem is closely related to your ...

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Constructing a space with prescribed cohomology ring
Accepted answer
3 votes

I did not understand exactly your question. What is important here, is the ring $k$. If $k=\mathbf{Z}$ then the problem you are asking for is hard, if $k$ is any commutative ring then the problem is ...

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Examples of unexpected mathematical images
28 votes

The spiral of prime numbers (white dots) the "pattern" is amazing, for an explanation of the picture you can take a look to this short youtube video.

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A general theory of quasi-functors, generalizing from dg-categories to $\mathcal V$-categories, with $\mathcal V$ monoidal model category
6 votes

I think the right way to call this functors is "quasi-representable" functors (in the language of Toen) and "potentially distinguished" functors in the language of Dwyer-Hess. At least when $\mathbf{...

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Motivation behind the definition of hochschild cohomology
Accepted answer
8 votes

I think you will have different answers to your questions. As you noticed there is more about Hochschild Homology in n-lab page and you also pointed out the interpretation of (positive) low dimension ...

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Why localize spaces with respect to homology?
7 votes

$\textbf{This is a point of view which means that it is only one side of the story}$. Let me start with Gel'fand theorem. The (opposite) category of compact Hausdorff spaces is equivalent to the ...

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Model structure of commutative dg-algebras inside all dg-algebras
1 votes

in the rational case, the forgetful functor U: dgCAlg-------> dgAlg induces a faithful functor in homotopy category under the following conditions. R is connected (connective) differential commutative ...

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Loop space of a category
3 votes

I will try to answer the question. As I said in a comment, the Thomason model structure on $Cat$ is not simplicial model structure. Let $C$ be a small category, we will view it as a topological ...

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Simplicial approximation for simplicial spaces
0 votes

I'm just reformulating your question in simplicial case. If you consider the category of simplicial sets $\mathbf{sSet}$ you can formulate your question as follows: Is the diagonal functor $diag: [\...

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