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14
votes
What are $( \infty , n)$-categories useful for?
In my humble opinion, the fact that such a structure appears naturally on bordisms between manifolds (eventually with some additional geometric structure like framings) is already a very good motivati …
8
votes
0
answers
240
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 …