234 We define the {\it support} of a blob diagram $b$, $\supp(b) \sub X$, 

   234 We define the {\it support} of a blob diagram $b$, $\supp(b) \sub X$, 

   235 to be the union of the blobs of $b$.

   235 to be the union of the blobs of $b$.

   236 For $y \in \bc_*(X)$ with $y = \sum c_i b_i$ ($c_i$ a non-zero number, $b_i$ a blob diagram),

   236 For $y \in \bc_*(X)$ with $y = \sum c_i b_i$ ($c_i$ a non-zero number, $b_i$ a blob diagram),

   237 we define $\supp(y) \deq \bigcup_i \supp(b_i)$.

   237 we define $\supp(y) \deq \bigcup_i \supp(b_i)$.

   238 

   238 

   239 We note that blob diagrams in $X$ have a structure similar to that of a simplicial set,

   240 We note that blob diagrams in $X$ have a structure similar to that of a simplicial set,

   240 but with simplices replaced by a more general class of combinatorial shapes.

   241 but with simplices replaced by a more general class of combinatorial shapes.

   241 Let $P$ be the minimal set of (isomorphisms classes of) polyhedra which is closed under products

   242 Let $P$ be the minimal set of (isomorphisms classes of) polyhedra which is closed under products

   242 and cones, and which contains the point.

   243 and cones, and which contains the point.

   243 We can associate an element $p(b)$ of $P$ to each blob diagram $b$ 

   244 We can associate an element $p(b)$ of $P$ to each blob diagram $b$ 

   252 For example, a diagram of $k$ strictly nested blobs corresponds to a $k$-simplex, while

   253 For example, a diagram of $k$ strictly nested blobs corresponds to a $k$-simplex, while

   253 a diagram of $k$ disjoint blobs corresponds to a $k$-cube.

   254 a diagram of $k$ disjoint blobs corresponds to a $k$-cube.

   254 (When the fields come from an $n$-category, this correspondence works best if we think of each twig label $u_i$ as having the form

   255 (When the fields come from an $n$-category, this correspondence works best if we think of each twig label $u_i$ as having the form

   255 $x - s(e(x))$, where $x$ is an arbitrary field on $B_i$, $e: \cF(B_i) \to C$ is the evaluation map, 

   256 $x - s(e(x))$, where $x$ is an arbitrary field on $B_i$, $e: \cF(B_i) \to C$ is the evaluation map, 

   256 and $s:C \to \cF(B_i)$ is some fixed section of $e$.)

   257 and $s:C \to \cF(B_i)$ is some fixed section of $e$.)