<\/p>\n
Hosted by the University of Leeds
\nSupported by the London Mathematical Society<\/p>\n
All talks are in the Roger Stevens Building, \u00a0Lecture Theatre 12 (Room 10M.12). It is located on Level 10, across the bridge from the School of Mathematics.<\/p>\n
Further information on travel to Leeds and the campus itself is available here:<\/p>\n
Speaker: Andrew Slattery<\/strong> Slides<\/b>: here<\/a><\/p>\n Speaker: Florrie Verity<\/strong> [1] F. William Lawvere (1969): Adjointness in Foundations. Dialectica 23, pp. 281\u2013296.
\nTitle: Property-like Structures and Relative Pseudomonads<\/strong>
\nAbstract:<\/strong> Idempotent monads\u2014monads for which T : C -> C is idempotent as a functor in the relevant category-theoretic sense, which is to say that mu : TT -> T is an isomorphism\u2014characterise monads whose algebras describe objects with only properties and not structure. Equivalently, the forgetful functor T-Alg -> C is fully faithful; every object of C has at most one algebra structure.
\nKock and Z\u00f6berlein independently developed the analogous notion in 2 dimensions (called KZ or lax-idempotent pseudomonads), which describe so-called \u201cproperty-like structures\u201d which are not quite unique but *are* unique up to unique isomorphism (as discussed by Kelly and Lack). For example, the pesudomonad whose algebras are categories with finite products (\u201chaving finite products\u201d being an example of a property-like structure) is lax-idempotent. One characterisation of lax-idempotency is that any algebra structure a : TA -> A is left adjoint to the unit i : A -> TA.
\nIn my talk I extend this characterisation to the relative setting, articulating analogues of two characterisations of lax-idempotency for relative pseudomonads and proving that they are equivalent.<\/p>\n
\nTitle: Hyperdoctrine semantics for higher-order modal logic<\/strong>
\nAbstract: <\/strong>Lawvere hyperdoctrines give categorical semantics for intuitionistic predicate logic [1]; they are flexible enough to be applied to other logics and can be extended to higher-order systems as higher-order hyperdoctrines (aka triposes). In this talk, I\u2019ll present a straightforward extension in both directions: sound and complete hyperdoctrine semantics for higher-order non-normal modal logics. By focusing on non-normal modal logics, this work is intended to complement the other categorical semantics that have been developed for modal predicate logic: namely, Ghilardi\u2019s first-order hyperdoctrine semantics for quantified normal modal logics [2]; and Awodey, Kishida and Kotzsch\u2019s topos semantics for higher-order intuitionistic S4 modal logic [3]. This is joint work with Yoshihiro Maruyama.<\/p>\n
\n[2] Torben Brauner & Silvio Ghilardi (2007): First-order modal logic. Studies in Logic and Practical Reasoning 3, pp. 549\u2013620.
\n[3] Steve Awodey, Kohei Kishida & Hans-Christoph Kotzsch (2014): Topos Semantics for Higher-Order Modal Logic. Logique et Analyse 57(228), pp. 591\u2013636.<\/p>\n