2
votes
0answers
83 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 ...
3
votes
1answer
327 views

Is there an analog of the Barratt-Eccles construction for group-like E_āˆž-spaces and E_āˆž-ring spaces?

The Barratt-Eccles operad is an operad in simplicial sets that provides a particularly nice model of an Eāˆž-operad; algebras in spaces over the Barratt-Eccles operad model Eāˆž-spaces, i.e., homotopy ...
4
votes
1answer
199 views

understanding the definition of $\infty$-operad of module objects

I'm just trying to understand the following definition: Definition 3.3.3.8 in Higher Algebra by J. Lurie defines the $\infty$-operad of $O$-module objects, and says the following: Let $O^\otimes$ be ...
1
vote
0answers
93 views

Exact sequence of L-infinity-algebras

We call a sequence of $L_\infty$-algebras (weak) maps $$0\to L\xrightarrow{f} M\xrightarrow{g} N\to 0$$ is exact if it is exact on the the underlying chain complexes level. Thought I don't know ...
3
votes
1answer
384 views

$A_{\infty}$ structure questions

Hello, I would like explanation or clear source for some things related to $A_{\infty}$-spaces, via Stasheff's polytopes. I tried not to think about them, because they seem too complicated for me; I ...