All Questions
9
questions
4
votes
0
answers
93
views
$E_k$-operads and actions on objects inside $k$-tuply monoidal $n$-category
I understood more or less the claim that $k$-tuply monoidal $n$-categories can be seen as $n$-categories equipped with an action of the $E_k$-operad.
For $k=2$, we have a homotopy equivalence $E_2(r) \...
- 1,743
3
votes
2
answers
240
views
Is the free algebra functor over an $\infty$-operad symmetric monoidal?
Suppose $F: \mathcal{O}^\otimes \to \mathcal{P}^\otimes$ is a map of $\infty$-operads, and $\mathcal{C}$ is a symmetric monoidal $\infty$-category that admits small colimits, such that the tensor ...
- 894
5
votes
0
answers
103
views
Is there a n-category structure on algebras for $e_n$-like operads?
I'm fishing in troubled waters here and therefore the question is vague and meant to be as general as possible. In particular "$e_n$-like operad" can be an algebraic or topological $e_n$ operad, as ...
- 2,034
9
votes
2
answers
390
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 ...
- 10.3k
6
votes
1
answer
352
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 ...
- 537
8
votes
0
answers
238
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 ...
- 1,589
10
votes
2
answers
956
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 ...
- 2,034
8
votes
0
answers
315
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 ...
- 27.3k
5
votes
1
answer
712
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 ...
- 37.2k