Mita Logic Seminar
Paul-André Melliès博士講演会

日時: 2006年9月14日 16:30〜18:00

場所: 三田東宝ビル8F人文COE会議室 (*場所等不明な方は慶大正門のガードマンにお尋ね下さい) (JR田町駅または都営地下鉄三田駅または赤羽橋駅(大江戸線)から 徒歩5分)
*建物の入口が常時ロックされておりますので, ドア脇のインターホンにて7Fの事務室又は8Fをお呼び出し下さい.

講演者: Paul-André Melliès (Chargé de Recherches CNRS)

タイトル: Functorial boxes in string diagrams

アブストラクト: String diagrams were introduced by Roger Penrose as a handy notation to manipulate morphisms in a monoidal category. In principle, this graphical notation should encompass the various pictorial systems introduced in proof-theory (like Jean-Yves Girard's proof-nets) and in concurrency theory (like Robin Milner's bigraphs). This is not the case however, at least because string diagrams do not accomodate boxes -- a key ingredient in these pictorial systems. In this talk, based on my accidental rediscovery of an idea by Robin Cockett and Robert Seely, I will explain how string diagrams may be extended with a notion of functorial box to depict a functor separating an inside world (its source category) from an outside world (its target category). I will expose two elementary applications of the notation: first, I will characterize graphically when a faithful balanced monoidal functor $F:C\longrightarrow D$ transports a trace operator from the category $D$ to the category $C$, which I exploit then to construct well-behaved parametric fixpoint operators in cartesian closed categories generated by models of linear logic; second, I will explain how the categorical semantics of linear logic indicates that the exponential box of proof-nets decomposes as *two* enshrined boxes.

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