equal
deleted
inserted
replaced
1091 \item elements $a_i\in \psi(x_i)$ and $b_i\in \psi(v_i)$, with $a_0 = a$ and $a_k = \hat{a}$, |
1091 \item elements $a_i\in \psi(x_i)$ and $b_i\in \psi(v_i)$, with $a_0 = a$ and $a_k = \hat{a}$, |
1092 such that $b_i$ and $b_{i+1}$both map to (glue up to) $a_i$. |
1092 such that $b_i$ and $b_{i+1}$both map to (glue up to) $a_i$. |
1093 \end{itemize} |
1093 \end{itemize} |
1094 In other words, we have a zig-zag of equivalences starting at $a$ and ending at $\hat{a}$. |
1094 In other words, we have a zig-zag of equivalences starting at $a$ and ending at $\hat{a}$. |
1095 The idea of the proof is to produce a similar zig-zag where everything antirefines to the same |
1095 The idea of the proof is to produce a similar zig-zag where everything antirefines to the same |
1096 disjoint union of balls, and then invoke the associativity axiom \ref{nca-assoc}. |
1096 disjoint union of balls, and then invoke Axiom \ref{nca-assoc} which ensures associativity. |
1097 \nn{hmmm... it would be nicer if this were ``7.xx" instead of ``4"} |
|
1098 |
1097 |
1099 Let $z$ be a decomposition of $W$ which is in general position with respect to all of the |
1098 Let $z$ be a decomposition of $W$ which is in general position with respect to all of the |
1100 $x_i$'s and $v_i$'s. |
1099 $x_i$'s and $v_i$'s. |
1101 There there decompositions $x'_i$ and $v'_i$ (for all $i$) such that |
1100 There there decompositions $x'_i$ and $v'_i$ (for all $i$) such that |
1102 \begin{itemize} |
1101 \begin{itemize} |