### lunck break

parent 0857c269
 ... ... @@ -2,6 +2,7 @@ \usepackage{mystyle} \begin{document} \chapter{Yoga of $\oo$-Categories : OLD} \section{$n$-graphs, $n$-magmas and $n$-categories} ... ... @@ -514,3 +515,4 @@ and we say that they are \emph{$k$-composable} for a $k< n$ if \todo{...} test \end{proof} \end{document}
 \chapter{Yoga of $\oo$-categories} \section{$\oo$-graphs, $\oo$-magmas and $\oo$-categories} \begin{paragr}\label{paragr:defngraph} An $\oo$-graph $C$ consists of an infinite sequence of sets $(X_k)_{k \in \mathbb{N}}$ together with maps An \emph{$\oo$-graph} $X$ consists of an infinite sequence of sets $(X_n)_{n \in \mathbb{N}}$ together with maps $\begin{tikzcd} X_{k} &\ar[l,"\src",shift left] \ar[l,"\trgt"',shift right] X_{k+1} X_{n} &\ar[l,"\src",shift left] \ar[l,"\trgt"',shift right] X_{n+1} \end{tikzcd}$ for every $k \in \mathbb{N}$, subject to the \emph{globular identities}: for every $n \in \mathbb{N}$, subject to the \emph{globular identities}: \begin{equation*} \left\{ \begin{aligned} ... ... @@ -15,13 +15,34 @@ \end{aligned} \right. \end{equation*} Elements of $X_k$ are called \emph{$k$-cells} or \emph{cells of dimension $k$}. For $x$ a $k$-cell with $k>0$, $\src(x)$ is the \emph{source} of $x$ and $\trgt(x)$ is the \emph{target} of $x$. More generally, for $0\leq i 0$, $\src(x)$ is the \emph{source} of $x$ and $\trgt(x)$ is the \emph{target} of $x$. More generally, for $0\leq k 0 \text{ and }\src(x)=\src(y) \text{ and } \trgt(x)=\trgt(y). \] Let$0 \leq k
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