A Representation Result for Free Cocompletions

John Power and Gian Luca Cattani and Glynn Winskel

Journal of Pure and Applied Algebra, vol. 151(3), pages 273-286, 2000.

Available as compressed DVI (24k) or postscript (96k).


Abstract

Given a class F of weights, one can consider the construction that takes a small category C to the free cocompletion of C under weighted colimits, for which the weight lies in F. Provided these free F-cocompletions are small, this construction generates a 2-monad on Cat, or more generally on V-Cat for monoidal biclosed complete and cocomplete V. We develop the notion of a dense 2-monad on V-Cat and characterise free F-cocompletions by dense KZ-monads on V- Cat. We prove various corollaries about the structure of such 2-monads and their Kleisli 2-categories, as needed for the use of open maps in giving an axiomatic study of bisimulation in concurrency. This requires the introduction of the concept of a pseudo-commutativity for a strong 2-monad on a symmetric monoidal 2-category, and a characterisation of it in terms of structure on the Kleisli 2-category


@article{power/cattani/winskel:reprfc,
  author =       {Power, A.~John and Cattani, Gian Luca and Winskel, Glynn},
  title =        {A Representation Result for Free Cocompletions},
  journal =      {Journal of Pure and Applied Algebra},
  volume =       {151},
  number=        3,
  year =         {2000}
  url =          {ftp://ftp.cl.cam.ac.uk/users/glc25/reprfc.ps.gz}
}

Home page / Papers
Gian Luca Cattani
Thu Jul 27 2000