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2 |
3 \section{Commutative algebras as $n$-categories} |
3 \section{Commutative algebras as $n$-categories} |
4 |
4 |
5 \nn{this should probably not be a section by itself. i'm just trying to write down the outline |
5 \nn{this should probably not be a section by itself. i'm just trying to write down the outline |
6 while it's still fresh in my mind.} |
6 while it's still fresh in my mind.} |
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7 |
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8 \nn{I strongly suspect that [blob complex |
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9 for $M^n$ based on comm alg $C$ thought of as an $n$-category] |
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10 is homotopy equivalent to [higher Hochschild complex for $M^n$ with coefficients in $C$]. |
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11 (Thomas Tradler's idea.) |
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12 Should prove (or at least conjecture) that here.} |
7 |
13 |
8 If $C$ is a commutative algebra it |
14 If $C$ is a commutative algebra it |
9 can (and will) also be thought of as an $n$-category whose $j$-morphisms are trivial for |
15 can (and will) also be thought of as an $n$-category whose $j$-morphisms are trivial for |
10 $j<n$ and whose $n$-morphisms are $C$. |
16 $j<n$ and whose $n$-morphisms are $C$. |
11 The goal of this \nn{subsection?} is to compute |
17 The goal of this \nn{subsection?} is to compute |