The formulas for composition of slices was wrong !

hmtpy.tex

@@ -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}