← rota-baxter-winning-games

TTIOS.tex

\begin{frame}\frametitle{This talk in one slide}
\begin{itemize}
    \item Basics of CGT: The \emph{generalized Bouton's theorem} allows us to decompose a game into smaller parts
    \item We prove 
    % \begin{center}
        \textbf{Games = \emph{Recursive $\Pf$-coalgebras}}
    % \end{center}
    \item As an application, we obtain a \emph{generalized generalized Bouton's theorem}, which may be a very powerful tool in CGT.
    % \item Post several open questions.
\end{itemize}

\begin{table}
    \centering
    \begin{tabular}{|c|c|} \hline 
         CGT&  CT\\ \hline 
         games&  $=$ recursive $\Pf$-coalgebras\\ \hline
 Winning/Losing state&$\in$ $\Pf$-algebra\\ \hline 
 Grundy number&$\in$ $\Pf$-algebra\\\hline
 Conway addition&$\in$ Monoidal structure\\ \hline 
 nim-sum (!?)&$\in$ \emph{Bouton monoid}\\\hline
 gen. Bouton's theorem&$\in$ gen. gen. Bouton's theorem!\\\hline
    \end{tabular}
    % \caption{Caption}
    % \label{tab:my_label}
\end{table}
\end{frame}