•  Krzysztof Worytkiewicz, Kathryn Hess, Paul-Eugène Parent and Andrew Tonks. A model structure à la Thomason for 2-Cat , to appear in Journal of Pure and Applied Algebra.
  
  We establish the existence of a Thomason-type, ``topological" model category structure on  2-Cat, the category of small 2-categories. Our methods are analogous to those of Thomason and Cisinski, though the generalization to 2-categories is nontrivial.
  
  
• Kathryn Hess, Paul-Eugène Parent, Andrew Tonks and Krzysztof Worytkiewicz. Simulations as homotopies, Electronic Notes in Theoretical Computer Science 100.
  
  A certain class of homotopies in the  Thomason-type, ``topological" model category structure on  2-Cat turns out to be in 1-to-1 correspondence with strong simulations among labeled transitions systems, formalising the geometric intuition of simulations as deformations. The correspondence still holds in the cubical setting, characterising simulations of higher-dimensional transition systems (HDTS).
  
  
• Krzysztof Worytkiewicz, Synchronization from a categorical perspective, preprint.
    
  We introduce a notion of synchronization for higher-dimensional automata, based on coskeletons of cubical sets. Categorification transports this notion to the setting of categorical transition systems. We apply the results to study the semantics of an imperative programming language with message-passing.
  

• Peter Bubenik and Krzysztof Worytkiewicz. A model category structure for local po-spaces. Homology, Homotopy and Applications, Vol. 8 (2006), No. 1, pp.263-292.
  
  Locally partial-ordered spaces (local po-spaces) have been used to model concurrent systems. We provide equivalences for these spaces by constructing a model category containing the category of local po-spaces. We show the category of simplicial presheaves on local po-spaces can be given Jardine's model structure, in which we identify the weak equivalences between local po-spaces. In the process we give an equivalence between the category of sheaves on a local po-space and the category of etale bundles over a local po-space. Finally we describe a localization that should provide a good framework for studying concurrent systems.