Definition Absolute equivalence of charts [efr-CTIK]

Let \mathcal {D} be a stochastic module over \mathcal {C}, and let \phi ,\phi ' be parallel morphisms in \mathsf {SChart}(\mathcal {D}). We say \phi ,\phi ' are absolutely equivalent if there exists a faithful strong Markov functor \mathcal {C} \hookrightarrow \mathcal {C}', and a faithful map of stochastic modules \mathcal {D} \hookrightarrow \mathcal {D}' (with \mathcal {D}' over \mathcal {C}) so that \phi ,\phi ' are identified by the induced map \mathsf {SChart}(\mathcal {D}) \to \mathsf {SChart}(\mathcal {D}')