Recursive coalgebras of finitary functors
For finitary set functors preserving inverse images, recursive coalgebras of Paul Taylor are proved to be precisely those for which the system described by always halts in finitely many steps.
A coalgebraic view on reachability
Coalgebras for an endofunctor provide a category theoretic framework for modeling a wide range of state-based systems of various types. We provide an iterative construction of the reachable part of a given pointed coalgebra that is inspired by and resembles the standard breadth-first search procedure to compute the reachable part of a graph. We also study coalgebras in Kleisli categories: for a functor extending a functor on the base category, we show that the reachable part of a given pointed coalgebra...
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