\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}