Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probability, valuations, hyperspace: Three monads on Top and the support
  as a morphism   We consider three monads on Top, the category of topological spaces, which
formalize topological aspects of probability and possibility in categorical
terms. The first one is the Hoare hyperspace monad H, which assigns to every
space its space of closed subsets equipped with the lower Vietoris topology.
The second is the monad V of continuous valuations, also known as the extended
probabilistic powerdomain. We construct both monads in a unified way in terms
of double dualization. This reveals a close analogy between them, and allows us
to prove that the operation of taking the support of a continuous valuation is
a morphism of monads from V to H. In particular, this implies that every
H-algebra (topological complete semilattice) is also a V-algebra. Third, we
show that V can be restricted to a submonad of tau-smooth probability measures
on Top. By composing these two morphisms of monads, we obtain that taking the
support of a tau-smooth probability measure is also a morphism of monads.

17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
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The categories of this paper are: stat