  Coalgebra is a currently quite active field, which aims to look at generic
state-based systems (most prominently automata) from a very abstract point of
view, mainly using tools from category theory. One of its achievements is to
give a completely generic approach of determinization, unifying in an elegant
manner non-deterministic automata, probabilistic automata or non-deterministic
pushdown automata in one and the same model. However, the case of alternating
automata fails to easily fit in this model. The aim of this internship was
therefore to tackle this problem: can alternating automata also be determinized
in the coalgebraic way? Does this give semantics that coincides with the
concretely defined one? In this report, we give a positive answer to both
questions. The main element of our construction is a distributive law, the
definition of which has been for some time an open question.
