Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
The Demonic Product of Probabilistic Relations
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
Bisimulation for labelled Markov processes
Information and Computation - Special issue: LICS'97
Approximating Labeled Markov Processes
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Semi-pullbacks and bisimulation in categories of Markov processes
Mathematical Structures in Computer Science
Factoring stochastic relations
Information Processing Letters
Semi-pullbacks for stochastic relations over analytic spaces
Mathematical Structures in Computer Science
Bisimulation and cocongruence for probabilistic systems
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Eilenberg--Moore algebras for stochastic relations
Information and Computation
Tracing Relations Probabilistically
Fundamenta Informaticae
Tracing Relations Probabilistically
Fundamenta Informaticae
Labelled Markov Processes: Stronger and Faster Approximations
Electronic Notes in Theoretical Computer Science (ENTCS)
Bisimulation and cocongruence for probabilistic systems
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Unprovability of the logical characterization of bisimulation
Information and Computation
Look: simple stochastic relations are just, well, simple
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
Congruences and bisimulations for continuous-time stochastic logic
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
Hyperfinite approximations to labeled markov transition systems
AMAST'06 Proceedings of the 11th international conference on Algebraic Methodology and Software Technology
Tracing Relations Probabilistically
Fundamenta Informaticae
Tracing Relations Probabilistically
Fundamenta Informaticae
Approximating Markov Processes by Averaging
Journal of the ACM (JACM)
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The problem of constructing a semi-pullback in a category is intimately connected to the problem of establishing the transitivity of bisimulations. Edalat shows that a semi-pullback can be constructed in the category of Markov processes on Polish spaces, when the underlying transition probability functions are universally measurable, and the morphisms are measure preserving continuous maps. We demonstrate that the simpler assumption of Borel measurability suffices. Markov processes are in fact a special case: we consider the category of stochastic relations over Standard Borel spaces. At the core of the present solution lies a selection argument from stochastic dynamic optimization. An example demonstrates that (weak) pullbacks do not exist in the category of Markov processes.