Links are user-specified data which transparently communicate what parts of the model can influence other parts of the model. Here, we're concerned with rewrite rules which can in principle have a different hazard rate for any state of the world. We wish to have the option to restrict the amount of information the hazard rate parameter has access to.
Embed the pattern in some larger context, $L \hookrightarrow Ctx$, and we pick out a subset $Dep \hookrightarrow Ctx$ where the relevant values the hazard rate is permitted to depend on are in $Dep$ (this latter mono might preferably be a map in $C$-Par, since it may not be a proper subobject).
State dependence would then be, rather than a function from $ACSet$ to probability measures, one has a function fomr $Dep^n$ to probability measures, where we have possibly $n$ maps from $Ctx \rightarrow World$ that commute with the match morphism $L \rightarrow World$.
Links are user-specified data which transparently communicate what parts of the model can influence other parts of the model. Here, we're concerned with rewrite rules which can in principle have a different hazard rate for any state of the world. We wish to have the option to restrict the amount of information the hazard rate parameter has access to.
Embed the pattern in some larger context, $L \hookrightarrow Ctx$, and we pick out a subset $Dep \hookrightarrow Ctx$ where the relevant values the hazard rate is permitted to depend on are in $Dep$ (this latter mono might preferably be a map in $C$-Par, since it may not be a proper subobject).
State dependence would then be, rather than a function from $ACSet$ to probability measures, one has a function fomr $Dep^n$ to probability measures, where we have possibly $n$ maps from $Ctx \rightarrow World$ that commute with the match morphism $L \rightarrow World$.