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Generalised species of structures and analytic functors

Nicola Gambino DPMMS University of Cambridge 4pm Tuesday 29 June 2004 Room 2511, JCMB, King's Buildings

The notions of species of structures and of analytic functor were introduced by Joyal to provide a rigorous foundation for the theory of formal power series, an important tool in enumerative combinatorics.

I will present a generalisation of Joyal's notions and explain how generalised species and analytic functors are related to ideas arising in theoretical computer science. In particular, there are connections to models of linear logic, Winskel's approach to concurrency, and Ehrhard and Regnier's differential lambda-calculus.

I will show how generalised species and analytic functors can be organized into a bicategory and a 2-category, respectively. Our main results show that these two-dimensional categories are equivalent and come equipped with a cartesian closed structure.

Joint work with Marcelo Fiore and Martin Hyland.

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