Definition \mathsf {BiSys}^M [efr-W413]

Let (\mathcal {C}, \mathcal {A}, T) be a stochastic dynamical systems theory. Consider the double category whose vertical category is \mathcal {C}_\mathrm {det} and horizontal category is \mathcal {C}, with commutative squares as the 2-cells (this is the transpose of \mathcal {C}^\to \rightrightarrows \mathcal {C}). This carries an obvious symmetric monoidal structure, and acts on the double category of stochastic arenas \widetilde {\mathsf {\mathbb Arena}}(\mathcal {A}) via the functor T. Denote by \mathsf {BiSys}^M(\mathcal {C},\mathcal {A},T) the symmetric monoidal triple category induced as in Definition [efr-EPI9] by this data.