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\title{Complete internal categories in toposes}
\author{Wouter Pieter Stekelenburg}\copyrightyear{2015}
\address{Faculty of Mathematics, Informatics and Mechanics\\
University of Warsaw\\
Banacha 2\\
02-097 Warszawa\\
Poland}
\eaddress{w.p.stekelenburg@gmail.com}
\keywords{realizability,topos}
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\begin{document}
\maketitle

\hide{
-goal
strong completeness of modest sets in asm_ex/lex

preservation of complete categories by ex/lex completions

-background
complete small categories are posets
complete internal categories in Grothendieck toposes are posets too

-strong and weak completeness

Not complete in every slice, only a dense subcategory where things are complete

-preservation of strong completeness by the ex/lex completion

}

\end{document}