Séminaire en ligne, 3 décembre 2020
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10h: accueil et problèmes de connexion 10h15: début de l'exposé 11h15: questions et discussion 12h: adieu et problèmes de déconnexion Merci aux auditeurs de couper micro et caméra (sauf éventuellement, lorsqu'ils souhaitent poser une question). Les questions peuvent aussi être posées dans la fenêtre de chat.
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Programme
- 10:00 – 12:00
-
Nicolas Blanco (Riverlane - University of Birmingham)
In this talk we will explore four different ways of interpreting classical multiplicative linear logic categorically: as a -autonomous category where the connectives are given by structures, as a -representable polycategory where the connectives are expressed through universal properties, as a bifibred polycategory where the connectives are recovered by fibrational properties and as a Frobenius pseudomonoid internal to a polycategory where the connectives are defined by internal operations. We will relate these approaches through different correspondences. First we will see that -representable polycategories are unbiased alternatives to the two-tensor polycategories with duals that have been introduced by Cockett and Seely and that has been proven to be equivalent to -autonomous categories. Then we will see that bifibred polycategories generalise those in the sense that a polycategory is -representable iff it is bifibred over the terminal polycategory. Finally, we will present a polycategorical Grothendieck correspondence between bifibrations of polycategories and pseudofunctors into MAdj, the 2-polycategory of multivariable adjunctions. When restricted to bifibrations over the terminal polycategory we get back the correspondence between -autonomous categories and Frobenius pseudomonoids in MAdj that was recently observed by Mike Shulman. If time permits we will also look at some refinements of *-autonomous categories by considering bifibred polycategories over a representable polycategory other than the terminal one.
