Proofs and algorithms seminar: Serge Lechenne on Wednesday 24 April 2024 at 14h00

===== Seminar of the proofs and algorithms pole =====

Hello everybody,

For a new seminar of the proofs and algorithms pole of LIX, we are happy to welcome Serge Lechenne (ENS Paris-Saclay), invited by the PARTOUT team.

***** Wednesday 24 April 2024 at 14h00, room Philippe Flajolet *****

Serge Lechenne -- Categorical structure in combinatorial algebras

We investigate a class of combinatory algebras, called ribbon combinatory algebras, in which we can interpret both the braided untyped linear lambda calculus and framed oriented tangles. Any reflexive object in a ribbon category gives rise to a ribbon combinatory algebra. Conversely, From a ribbon combinatory algebra we can construct a ribbon category with a reflexive object, from which the combinatory algebra can be recovered. To show this, and also to give the equational characterization of ribbon combinatory algebras, we make use of the internal PRO construction developed in Hasegawa’s recent work. Interestingly, we can characterize ribbon combinatory algebras in two different ways: as balanced combinatory algebras with a trace combinator, and as balanced combinatory algebras with duality.


The following seminar will be on Friday 26 April 2024 at 10h30 by Vikraman Choudhury: Symmetries in constructive mathematics.

The list of upcoming seminars can be found at:
https://www.lix.polytechnique.fr/proofs-algorithms/seminar/

The calendar of seminars can be found at:
https://www.lix.polytechnique.fr/proofs-algorithms/seminar/calendar.ics