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-
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
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