This book constitutes the thoroughly refereed post-conference proceedings of the 13th International Workshop on Coalgebraic Methods in Computer Science, CMCS 2016, colocated with ETAPS 2016, held in Eindhoven, The Netherlands, in April 2016.

The 10 revised full papers were carefully reviewed and selected from 13 submissions. Also included are an invited paper and two keynote talks. The papers cover a wide range of topics in the theory, logics and applications of coalgebras.

Fixed Points of Functors - A Survey.- Compositional Coinduction with Sized Types.- Lawvere Theories as Composed PROPs.- Transitivity and Difunctionality of Bisimulations.- Affine Monads and Side-Effect-Freeness.- Duality of Equations and Coequations via Contravariant Adjunctions.- Category Theoretic Semantics for Theorem Proving in Logic Programming: Embracing the Laxness.- Product Rules and Distributive Laws.- On the Logic of Generalised Metric Spaces.- A Complete Logic for Behavioural Equivalence in Coalgebras of Finitary Set Functors.- Coalgebraic Completeness-via-Canonicity: Principles and Applications.- Relational Lattices via Duality.- On Local Characterization of Global Timed Bisimulation for Abstract.