PGames

Definition 1.1 (Partisan games)§

Write $T=\mathcal{P}_{\mathrm{fin}}\times\mathcal{P}_{\mathrm{fin}}$. PGames is the category of recursive coalgebras $\theta=(\theta^L,\theta^R):X\to T(X)$ and coalgebra morphisms. Here $\theta^L(x)$ and $\theta^R(x)$ are the options of Left and Right at $x$. Recursive means that for every algebra $\alpha:T(A)\to A$ there is a unique function $f:X\to A$ with $f=\alpha\circ T(f)\circ\theta$.