Commit 9a578f87 authored by Leonard Guetta's avatar Leonard Guetta
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I did not do much today

parent 298d099e
...@@ -206,7 +206,7 @@ ...@@ -206,7 +206,7 @@
\end{enumerate} \end{enumerate}
We will use the same letter to denote an $n$-category and its underlying $n$-magma. Let $C$ and $C'$ be $n$-categories, a \emph{morphism of $n$-categories} (or $n$-functor) $f : C \to C'$ is simply a morphism of $n$-magmas. We denote by $n\Cat$ the category of $n$-categories and morphisms of $n$-categories. We will use the same letter to denote an $n$-category and its underlying $n$-magma. Let $C$ and $C'$ be $n$-categories, a \emph{morphism of $n$-categories} (or $n$-functor) $f : C \to C'$ is simply a morphism of $n$-magmas. We denote by $n\Cat$ the category of $n$-categories and morphisms of $n$-categories.
\end{paragr} \end{paragr}
\begin{paragr} \begin{paragr}\label{paragr:defoocat}
Once again, for any $n>0$ there is a canonical ``truncation'' functor Once again, for any $n>0$ there is a canonical ``truncation'' functor
\[ \[
n\Cat \to (n \shortminus 1)\Cat n\Cat \to (n \shortminus 1)\Cat
...@@ -232,6 +232,18 @@ ...@@ -232,6 +232,18 @@
\] \]
which is easily seen to be full. which is easily seen to be full.
\end{paragr} \end{paragr}
\begin{paragr}
For any $n>0$, let us denote $\tau$ the canonical truncation functor
\[
\tau : n\Cat \to (n \shortminus 1)\Cat
\]
from Paragraph \ref{paragr:defoocat} and
\[
\tau_{\leq n} : \oo\Cat \to n\Cat
\]
the canonical arrow of the limiting cone from the same paragraph.
Let $C$ be a $(n\shortminus 1)$-category. We define a category $C'$
\end{paragr}
\begin{paragr} \begin{paragr}
Let $n>0$, we define the category $n\GCat$ as the following fibred product Let $n>0$, we define the category $n\GCat$ as the following fibred product
\[ \[
......
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