405 research outputs found
Behavioural equivalences for timed systems
Timed transition systems are behavioural models that include an explicit
treatment of time flow and are used to formalise the semantics of several
foundational process calculi and automata. Despite their relevance, a general
mathematical characterisation of timed transition systems and their behavioural
theory is still missing. We introduce the first uniform framework for timed
behavioural models that encompasses known behavioural equivalences such as
timed bisimulations, timed language equivalences as well as their weak and
time-abstract counterparts. All these notions of equivalences are naturally
organised by their discriminating power in a spectrum. We prove that this
result does not depend on the type of the systems under scrutiny: it holds for
any generalisation of timed transition system. We instantiate our framework to
timed transition systems and their quantitative extensions such as timed
probabilistic systems
The homotopy theory of strong homotopy algebras and bialgebras
Lada introduced strong homotopy algebras to describe the structures on a
deformation retract of an algebra in topological spaces. However, there is no
satisfactory general definition of a morphism of strong homotopy (s.h.)
algebras. Given a monad T on a simplicial category C, we instead show how s.h.
T-algebras over C naturally form a Segal space. Given a distributive
monad-comonad pair (T, S), the same is true for s.h. (T, S)-bialgebras over C;
in particular this yields the homotopy theory of s.h. sheaves of s.h. rings.
There are similar statements for quasi-monads and quasi-comonads. We also show
how the structures arising are related to derived connections on bundles.Comment: 58 pages; v2 final version, to appear in HHA
Note on star-autonomous comonads
We develop an alternative approach to star-autonomous comonads via linearly
distributive categories. It is shown that in the autonomous case the notions of
star-autonomous comonad and Hopf comonad coincide.Comment: 9 page
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