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      7
      votes
      1answer
      217 views

      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 ...
      2
      votes
      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 ...
      5
      votes
      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 ...
      8
      votes
      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 ...
      11
      votes
      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/...
      8
      votes
      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 ...
      8
      votes
      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 ...
      6
      votes
      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 ...
      10
      votes
      1answer
      584 views

      $k$-Disk algebras versus $E_k$ algebras

      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\...
      5
      votes
      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 ...
      0
      votes
      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 ...
      8
      votes
      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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