理論計算機科学と圏論ワークショップ
Workshop on Computer Science and Category Theory
CSCAT 2010
プログラム/Program

3月18日 5階 第3演習室/18th Mar at Ensyushitsu 3

• 10:30- 蓮尾 一郎（京都大学）/ Ichiro Hasuo (Kyoto univ.)
  題目: Component Calculi via the Microcosm Interpretation of GSOS Rules
  概要: We extend the well-developed framework of structural operational semantics (SOS) into another dimension. Focusing on well-behaved 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 so-called the microcosm principle. The framework can also be seen as a 2-dimensional extension of the bialgebraic modeling of SOS originated by Rutten, Turi and Plotkin.
• 11:30- 浅田 和之（京都大学）/ Kazuyuki Asada (Kyoto univ.)
  題目: Categorifying Computations into Components via Arrows as Profunctors.
  概要: 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 state-based systems as components―in fact, it is a categorified version of arrow that does so. In this paper, following the second author’s previous work with Heunen, Jacobs and Sokolova, we prove that a certain coalgebraic modeling of components― which generalizes Barbosa’s―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 author’s 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.)
• 12:30-2:00 昼食休憩
• 2:00- 長谷川 真人（京都大学）/ Masahito Hasegawa (Kyoto univ.)
  題目: A Quantum Double Construction in Rel
  概要: For any group G, we derive a ribbon category of crossed G-sets 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- 長谷川 立（東京大学）/ Ryu Hasegawa (Univ. of Tokyo)
  題目: リニアカテゴリ上の計算体系 LC のチャーチ・ロッサー性について：部分的解決
• 4:00- 平井　洋一（東京大学）/ Youichi Hirai (Univ. of Tokyo)
  題目: Investigations on intuitionistic modal logics towards completeness for the finite sequential Kripke models.

3月19日 2階 第2会議室 / 19th Mar at Kaigishitsu 2

• 10:30- 西澤 弘毅（鳥取環境大学）/ Koki Nishizawa (Tottori Environment univ.)
  題目: Co-fibrational generalisation of Stone-type adjunctions
• 11:30- 丸山 善宏（京都大学）/ Yoshihiro Maruyama (Kyoto univ.)
  題目: Quasi-Variety Modalized: Topological and Coalgebraic Study
  概要: The theory of natural dualities by Davey, Priestley and others is a general theory of Stone-type dualities based on the machinery of universal algebra. In this talk, by proposing the notion of modal quasi-variety, we extend the theory of natural dualities so that it encompasses Jonsson-Tarski duality and Kupke-Kurz-Venema coalgebraic duality for modal algebras.
• 12:30-2:00 昼食休憩
• 2:00- 白旗 優（慶應義塾大学）Masaru Shirahata (Keio univ.)
• 3:00- 星野 直彦（京都大学）Naohiko Hoshino (Kyoto univ.)
• 4:00- 角谷　良彦（東京大学）/ Yoshihiko Kakutani (Uinv. of Tokyo)