@@ -315,7 +315,9 @@ From now on, we will consider that the category $\Psh{\Delta}$ is equipped with
\end{paragr}
\begin{paragr}\label{paragr:formulasoplax}[Formulas for oplax transformations] We now give a third way of describing oplax transformations based on explicit formulas. The proof that this description is equivalent to those given in the previous paragraph can be found in \cite[Appendice B.2]{ara2016joint}.
\begin{paragr}\label{paragr:formulasoplax}[Formulas for oplax
transformations] We now give a third way of describing oplax
transformations based on explicit formulas. The proof that this description is equivalent to those given in the previous paragraph can be found in \cite[Appendice B.2]{ara2016joint}.
Let $u, v : X \to Y$ two $\oo$\nbd{}functors. An oplax transformation $\alpha : u \Rightarrow v$ is given by the data of:
\begin{itemize}[label=-]
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@@ -340,7 +342,9 @@ From now on, we will consider that the category $\Psh{\Delta}$ is equipped with
\]
\end{enumerate}
\end{itemize}
\end{itemize}
Note that to read the formulas correctly, one has to remember the
convention that for $k<n$, the composition $\comp_k$ has priority over $\comp_n$ (see \ref{paragr:defoomagma}).
\end{paragr}
\begin{example}\label{example:natisoplax}
When $C$ and $D$ are $n$\nbd{}categories with $n$ finite and $u,v :C \to D$ are two $n$\nbd{}functors, an oplax transformation $\alpha : u \Rightarrow v$ amounts to the data of a $(k+1)$\nbd{}cell $\alpha_x$ of $D$ for each $k$\nbd{}cell $x$ of $C$ with $0\leq k \leq n$, with source and target as in the previous paragraph. These data being subject to the axioms of the previous paragraph. Note that when $x$ is an $n$\nbd{}cell of $C$, $\alpha_x$ is necessarily a unit, which can be expressed as the equality
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@@ -748,7 +752,7 @@ The nerve functor $N_{\omega} : \omega\Cat \to \Psh{\Delta}$ sends the equivalen