The first international workshop on Pomsets and Related Structures took place at EPITA Rennes on 24 April 2024.
The workshop is associated with the (i)Po(m)set Project, a research project at the crossroads of concurrency theory, automata theory, algebra, and geometry. Its 2024 edition was collocated with ATLAS'24 and was followed by the Journées GT DAAL.
Henning Basold,
Universiteit Leiden, The Netherlands:
Simplicial and Higher Coalgebras
There is an intricate link between concurrent systems and
homotopy theory that has been exploited, for instance, in
higher-dimensional automata and their languages. An
abstraction of computation is the theory of coalgebra, which
provides a general understanding of step-wise computation,
global behaviour, modal logic and many other concepts of
computation and reasoning. In this talk, I will provide first
an introduction to coalgebra in the setting of simplicial sets
and how concurrent computing can be understood there, albeit
being limited to the deterministic case for the time being.
We will then discuss what the roadblock to a coalgebraic view
on true concurrency with non-deterministic branching is.
After this, we will see that the link between computation and
homotopy theory goes very deep. This merits an abstract
development of homotopy theory for computation, for which I
will sketch an outline in the form of higher coalgebra, which
I understand as coalgebra in the context of higher categories.
We will discuss the intuition and ingredients that go into
such a theory, which will bring us back to coalgebras on
simplicial sets.
Online participants: