# A Coalgebraic View on Reachability

## TL;DR

This paper introduces a coalgebraic framework for modeling state-based systems and presents an iterative method, inspired by BFS, to compute the reachable part of coalgebras, including in Kleisli categories.

## Contribution

It provides a novel iterative construction for reachability in coalgebras, extending classical methods to a categorical setting and including Kleisli categories.

## Key findings

- The iterative construction generalizes BFS for coalgebras.
- Reachability can be computed in Kleisli categories for extended functors.
- The approach unifies various state-based system models under a coalgebraic framework.

## Abstract

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 can be computed in that base category.