Important Work

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The intention of having this page is to collect important pieces of work, must-reads if you will, in the area of coalgebra. This should help people that are new in the field or want to learn about it to orient themselves. It might even provide some new references and ideas for those being actively involved in the field of coalgebra.

The page is divided in subfields and should, besides the reference itself, also give a short description of the papers at hand.


  • J. Rutten, ‘Universal Coalgebra: A Theory of Systems’. DBLP DOI

This is certainly a classical reference to the modern view on state-based system through the eyes of coalgebra. The paper contains many important results that resemble results in universal algebra, hence the title. These results are proven in the category Set of sets but the proofs often rely on principles that are also available in other categories. For example, the notion of bisimulations can be recovered in many important cases, see Sam Statons work below.

  • S. Staton, ‘Relating coalgebraic notions of bisimulation’. DBLP DOI

This paper gives a very nice and coherent overview of possible notions of bisimulation and behavioural equivalence, and how they relate. In total, four such notions are related by establishing the additional assumptions one has to make on the category and/or functors to show that equivalence due to one notion implies another. All this is nicely summarised in a diagram.

Automata Theory[edit]

Coalgebraic Logic[edit]


Probabilistic Systems[edit]

Programming Languages[edit]


Theorem Proving[edit]

Quantum Systems[edit]