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# All Questions

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1answer
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### Monoidal structures on modules over derived coalgebras

Given a Hopf-algebra $H$ (over a commutative ring), it is a classical fact that its category of (left) modules is monoidal, even if $H$ is not commutative. Given two left modules $M$ and $N$, we can ...
1answer
99 views

### Pseudo or lax algebras for a 2-monad, reference request

I would like to find explicit definitions of pseudo, or even lax, algebras for a 2-monad, and their lax morphisms, with all the coherence diagrams included. Alternatively, coherent lax algebras for ...
1answer
241 views

### Monadic interpretation of coalgebras over operads

The structure of an algebra $A$ over a operad $O$ is encoded by an operad morphisms from $O$ to $\{Hom(A^{\otimes k},\, A)\}_{k}$. The same structure can be stored using the structure $M_OA\to A$ of ...
0answers
210 views

### Framed higher Hochschild cohomology

Given an $E_n$-algebra $A$, one can define its $E_n$-Hochschild complex $CH_{E_n}(A,A)$ by the formula $$Ch_{E_n}(A,A)=RHom_{Mod_A^{E_n}}(A,A)$$ where $Mod_A^{E_n}$ is the category of $A$-modules over ...
0answers
317 views

### Is the operadic nerve functor an equivalence of ∞-categories?

It is now known that the $\infty$-category of $\infty$-operads as defined by Lurie is equivalent to the underlying $\infty$-category of the model category of simplicial operads, see http://arxiv.org/...
2answers
638 views

### What are algebras for the little n-balls/n-cubes/n-something operads exactly?

As a non expert in the theory of topological operads, I find it pretty hard, to understand what algebras for little balls/cubes/something operads are. For all the other famous operads I know (like ...
0answers
305 views

### A model category for E-infty algebras in a non-monoidal model category?

Given a suitable nice symmetric monoidal category $C$, symmetric monoidally enriched, tensored, and cotensored over a symmetric monoidal category $S$, and an operad $\mathcal{O}$ in $S$, we can ...
2answers
514 views

### Obstructions for $E_n$-algebras

In Alan Robinson's paper, Classical Obstructions and S-algebras, he provides conditions for a ring spectrum to have an $A_n$ and $\mathbb{E}_\infty$-structure. Have the obstructions for an object ...
1answer
584 views

Background: The little $k$-cubes operad is the $(\infty,1)$-operad defined by embedding disjoint unions of $k$-dimensional open cubes rectilinearly into one another, that is using maps $(0,1)^k\... 1answer 588 views ### Which E_∞-spaces are homotopy colimits of k-truncated E_∞-spaces? This question is closely related to my previous question about modules over truncated sphere spectra, in particular, it has the same motivation. Recall that every space (or ∞-groupoid) can be ... 0answers 380 views ### []-infinity algebra and Projective representation This is a very vague question. We know that some algebra structures can be viewed as modules of some fantastic stuff, call T. Such examples include: Abelian groups are$\mathbb{Z}$-modules, chain ... 1answer 543 views ### Is there a “derived” Free$P$-algebra functor for an operad$P$? Recall that an operad (in vector spaces, say)$P$consists of a collection of vector spaces$P(n)$for$n\geq 0$, such that$P(n)$is equipped with an action by the symmetric group$S_n$, with maps$P(...

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