Commit f203e5c7 authored by Leonard Guetta's avatar Leonard Guetta
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The formulas for composition of slices was wrong !

parent 7f52396e
......@@ -795,8 +795,8 @@ The nerve functor $N_{\omega} : \omega\Cat \to \Psh{\Delta}$ sends the equivalen
\begin{tabular}{ll}
$z_{i}=y_i\comp_k x_i$, & for every $k+1 \leq i \leq n$, \\[0.75em]
$z'_i=y'_i \comp_k x'_i$, & for every $k+1 \leq i \leq n-1$, \\[0.75em]
$c_i=a_i\comp_k b_i \comp_{k-1} a'_{k-1} \comp_{k-2} a'_{k-2} \comp_{k-3} \cdots \comp_{1} a'_1\comp_0 x_k$,&for every $k+1 \leq i \leq n+1$, \\[0.75em]
$c'_i=a'_i\comp_k b'_i \comp_{k-1} a'_{k-1} \comp_{k-2} a'_{k-2} \comp_{k-3} \cdots \comp_{1} a'_1\comp_0 x'_k$,&for every $k+1 \leq i \leq n$.\\
$c_i=a_i\comp_{k+1} b_i \comp_{k} a'_{k} \comp_{k-1} a'_{k-1} \comp_{k-2} \cdots \comp_{1} a'_1\comp_0 x_k$,&for every $k+2 \leq i \leq n+1$, \\[0.75em]
$c'_i=a'_i\comp_{k+1} b'_i \comp_{k} a'_{k} \comp_{k-1} a'_{k-1} \comp_{k-2} \cdots \comp_{1} a'_1\comp_0 x'_k$,&for every $k+2 \leq i \leq n$.\\
\end{tabular}
\end{itemize}
We leave it to the reader to check that the formulas are well defined and that the axioms for $\oo$\nbd{}categories are satisfied. The canonical forgetful $\oo$\nbd{}functor $\pi : A/a_0 \to A$ is simply expressed as:
......@@ -839,7 +839,6 @@ The nerve functor $N_{\omega} : \omega\Cat \to \Psh{\Delta}$ sends the equivalen
\end{tabular}
and the $b_i$ and $b'_i$ are $i$-cells of $B$ such that
\[
\begin{pmatrix}
\begin{matrix}
......
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