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Results tagged with operads
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user 6936
2
votes
Accepted
$\mathbb{E}_M$ as colimit of little cubes operads
I claim that, if $X$ is a groupoid, then the category of $X$-families of operads is the same as the category of functors $\mathsf{Fun}(X, \mathsf{Op})$. … But now the definition of an $X$-family of operads corresponds exactly to the requirement that the functor from $X$ to $\mathsf{Cat}\downarrow \mathsf{Fin}_*$ factors through the subcategory of operads …
- 13.5k
9
votes
Accepted
How to characterize $E_n$ morphisms from $\mathrm{Mod}(A)$ to $\mathrm{Mod}(B)$?
By Corollary HA.4.8.5.20, the functor from $\mathbb{E}_{n+1}$-algebras to $\mathbb{E}_n$-monoidal categories and colimit-preserving, $\mathbb{E}_n$-monoidal functors is fully faithful. (Notice that th …
- 13.5k
7
votes
Accepted
Homotopy invariant structure: Stasheff versus Segal
As requested, my comments in the form of an answer:
At the end of Categories and Cohomology Theories Segal gives a fairly detailed sketch of how to compare these theories in the harder, $\mathbb{E}_{ …
- 13.5k
14
votes
Accepted
Obstructions for $E_n$-algebras
Let me expand a little on what Qiaochu and Craig mentioned.
If you want an obstruction theory for building an uber-gadget, you'll need (i) an algebraic approximation to such gadgets, and (ii) a way t …
- 13.5k