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For questions involving one or more categorical dimensions, or involving homotopy coherent categorical structures.

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 …
Sinan Yalin's user avatar
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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 …
Sinan Yalin's user avatar
  • 1,609