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Fix empty topos
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aisejohan committed Sep 2, 2019
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Expand Up @@ -2841,14 +2841,14 @@ \section{Topoi}
use this abuse of notation.

\medskip\noindent
Two examples of topoi. The {\it empty topos} is topos
of sheaves on the site $\mathcal{C}$, where $\mathcal{C}$ has
a single object $\emptyset$ and a single morphism $\text{id}_\emptyset$
and a single covering, namely the empty covering of $\emptyset$.
We will sometimes write $\emptyset$ for this site.
This is a site and every sheaf on $\mathcal{C}$ assigns a singleton to
$\emptyset$. Thus $\Sh(\emptyset)$ is equivalent to the category
The {\it empty topos} is topos
of sheaves on the site $\mathcal{C}$, where $\mathcal{C}$
is the empty category. We will sometimes write $\emptyset$ for this site.
This is a site which has a unique sheaf (since $\emptyset$ has no
objects). Thus $\Sh(\emptyset)$ is equivalent to the category
having a single object and a single morphism.

\medskip\noindent
The {\it punctual topos} is the topos of sheaves on the site
$\mathcal{C}$ which has a single object $pt$ and one morphism
$\text{id}_{pt}$ and whose only covering is the covering
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