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Workshop on Computer Science and Category Theory
CSCAT 2010
vO/Program
318ϊ 5K ζ3KΊ/18th Mar at Ensyushitsu 3

10:30 @φ κYisεwj/ Ichiro Hasuo (Kyoto univ.)
θΪ: Component Calculi via the Microcosm Interpretation of GSOS Rules
Tv: We extend the welldeveloped framework of structural operational
semantics (SOS) into another dimension. Focusing on wellbehaved GSOS
rules, we present their new interpretation that derives process
operators on labeled transition systems themselves. This turns a
process calculus into a component calculus. The conventional
interpretation which derives transition structure on the set of
process terms arises canonically from our new interpretation. Relating
the two interpretations is our general compositionality result that
supports modular design of systems. We exploit a categorical viewpoint
that the two interpretations of GSOS rules realize nested algebraic
structure, an instance of socalled the microcosm principle. The
framework can also be seen as a 2dimensional extension of the
bialgebraic modeling of SOS originated by Rutten, Turi and Plotkin.

11:30 σc aVisεwj/ Kazuyuki Asada (Kyoto univ.)
θΪ: Categorifying Computations into Components via Arrows as Profunctors.
Tv: The notion of arrow by Hughes is an axiomatization of the
algebraic structure possessed by structured computations in
general. We claim that an arrow also serves as a basic component
calculus for composing statebased systems as components\in fact, it
is a categorified version of arrow that does so. In this paper,
following the second authorfs previous work with Heunen, Jacobs and
Sokolova, we prove that a certain coalgebraic modeling of components\
which generalizes Barbosafs\indeed carries such arrow structure.
Our coalgebraic modeling of components is parametrized by an arrow A
that specifies computational structure exhibited by components; it
turns out that it is this arrow structure of A that is lifted and
realizes the (categorified) arrow structure on components. The lifting
is described using the first authorfs recent characterization of an
arrow as an internal strong monad in Prof , the bicategory of small
categories and profunctors.
(This is joint work with Ichiro Hasuo.)
 12:302:00 Hxe
 2:00 ·Jμ ^lisεwj/ Masahito Hasegawa (Kyoto univ.)
θΪ: A Quantum Double Construction in Rel
Tv: For any group G, we derive a ribbon category of crossed Gsets
as the category of modules of a Hopf algebra in the compact
closed category Rel of sets and functions. The Hopf algebra
is obtained by the quantum double construction of Drinfel'd.
 3:00 ·Jμ §iεwj/ Ryu Hasegawa (Univ. of Tokyo)
θΪ: jAJeSγΜvZΜn LC Μ`[`EbT[«ΙΒ’ΔFͺIπ
 4:00 ½δ@mκiεwj/ Youichi Hirai (Univ. of Tokyo)
θΪ: Investigations on intuitionistic modal logics towards completeness for the finite sequential Kripke models.
319ϊ 2K ζ2οcΊ / 19th Mar at Kaigishitsu 2
 10:30 ΌΰV OBiΉζΒ«εwj/ Koki Nishizawa (Tottori Environment univ.)
θΪ: Cofibrational generalisation of Stonetype adjunctions
 11:30 ΫR PGisεwj/ Yoshihiro Maruyama (Kyoto univ.)
θΪ: QuasiVariety Modalized: Topological and Coalgebraic Study
Tv: The theory of natural dualities by Davey, Priestley and others
is a general theory of Stonetype dualities based on the machinery of
universal algebra. In this talk, by proposing the notion of modal
quasivariety, we extend the theory of natural dualities so that it
encompasses JonssonTarski duality and KupkeKurzVenema coalgebraic
duality for modal algebras.
 12:302:00 Hxe
 2:00 ψ Dicδ`mεwjMasaru Shirahata (Keio univ.)
 3:00 ―μ ΌFisεwjNaohiko Hoshino (Kyoto univ.)
 4:00 pJ@ΗFiεwj/ Yoshihiko Kakutani (Uinv. of Tokyo)
2010/3/16