Cédric de Lacroix
LIS, Aix-Marseille Université
https://www.researchgate.net/profile/Cedric-De-Lacroix
Date(s) : 17/11/2022 iCal
11 h 00 min - 12 h 30 min
It is known that the quantale of sup-preserving maps from a complete lattice to itself is a Frobenius quantale if and only if the lattice is completely distributive. Since completely distributive lattices are the nuclear objects in the autonomous category of complete lattices and sup-preserving maps, we study the above statement in a categorical setting. We introduce the notion of Frobenius structure in an arbitrary autonomous category, generalizing that of Frobenius quantale. We prove that the monoid of endomorphisms of a nuclear object has a Frobenius structure. If the environment category is star-autonomous and has epi-mono factorizations, a variant of this theorem allows to develop an abstract phase semantics and to generalise the previous statement. Conversely, we argue that, in a star-autonomous category where the monoidal unit is a dualizing object, if the monoid of endomorphisms of an object has a Frobenius structure and the monoidal unit embeds into this object as a retract, then the object is nuclear.
Slides : https://pageperso.lis-lab.fr/~cedric.de-lacroix-de-lavalette/diapo/diapo_ldp_17112022.pdf
L’exposé sera également retransmis ici :
https://greenlight.lal.cloud.math.cnrs.fr/b/lio-hdc-jef
Emplacement
Site Sud, Luminy, Ancienne BU, Salle Séminaire2 (RdC)
Catégories