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197 \begin{itemize} |
197 \begin{itemize} |
198 \item $p(\emptyset) = pt$, where $\emptyset$ denotes a 0-blob diagram or empty tree; |
198 \item $p(\emptyset) = pt$, where $\emptyset$ denotes a 0-blob diagram or empty tree; |
199 \item $p(a \du b) = p(a) \times p(b)$, where $a \du b$ denotes the distant (non-overlapping) union of two blob diagrams (equivalently, join two trees at the roots); and |
199 \item $p(a \du b) = p(a) \times p(b)$, where $a \du b$ denotes the distant (non-overlapping) union of two blob diagrams (equivalently, join two trees at the roots); and |
200 \item $p(\bar{b}) = \kone(p(b))$, where $\bar{b}$ is obtained from $b$ by adding an outer blob which encloses all the others. |
200 \item $p(\bar{b}) = \kone(p(b))$, where $\bar{b}$ is obtained from $b$ by adding an outer blob which encloses all the others. |
201 \end{itemize} |
201 \end{itemize} |
202 (This correspondence works best if we thing of each twig label $u_i$ as being a difference of |
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203 two fields.) |
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204 For example, a diagram of $k$ strictly nested blobs corresponds to a $k$-simplex, while |
202 For example, a diagram of $k$ strictly nested blobs corresponds to a $k$-simplex, while |
205 a diagram of $k$ disjoint blobs corresponds to a $k$-cube. |
203 a diagram of $k$ disjoint blobs corresponds to a $k$-cube. |
206 |
204 (This correspondence works best if we thing of each twig label $u_i$ as having the form |
207 |
205 $x - s(e(x))$, where $x$ is an arbitrary field on $B_i$, $e: \cC(B_i) \to C$ is the evaluation map, |
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206 and $s:C \to \cC(B_i)$ is some fixed section of $e$.) |
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207 |
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208 |