equal
deleted
inserted
replaced
5 |
5 |
6 So far we have provided no evidence that blob homology is interesting in degrees |
6 So far we have provided no evidence that blob homology is interesting in degrees |
7 greater than zero. |
7 greater than zero. |
8 In this section we analyze the blob complex in dimension $n=1$. |
8 In this section we analyze the blob complex in dimension $n=1$. |
9 We find that $\bc_*(S^1, \cC)$ is homotopy equivalent to the |
9 We find that $\bc_*(S^1, \cC)$ is homotopy equivalent to the |
10 Hochschild complex of the 1-category $\cC$. |
10 Hochschild complex of the 1-category $\cC$. (Recall from \S \ref{sec:example:traditional-n-categories(fields)} that a $1$-category gives rise to a $1$-dimensional system of fields; as usual, talking about the blob complex with coefficients in a $n$-category means first passing to the corresponding $n$ dimensional system of fields.) |
11 \nn{cat vs fields --- need to make sure this is clear} |
|
12 Thus the blob complex is a natural generalization of something already |
11 Thus the blob complex is a natural generalization of something already |
13 known to be interesting in higher homological degrees. |
12 known to be interesting in higher homological degrees. |
14 |
13 |
15 It is also worth noting that the original idea for the blob complex came from trying |
14 It is also worth noting that the original idea for the blob complex came from trying |
16 to find a more ``local" description of the Hochschild complex. |
15 to find a more ``local" description of the Hochschild complex. |