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UID:5885@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20221117T110000
DTEND;TZID=Europe/Paris:20221117T123000
DTSTAMP:20241120T200647Z
URL:https://www.i2m.univ-amu.fr/evenements/frobenius-structure-in-star-aut
 onomous-categories/
SUMMARY:Cédric de Lacroix (LIS\, Aix-Marseille Université): Frobenius str
 ucture in star-autonomous categories
DESCRIPTION:Cédric de Lacroix: It is known that the quantale of sup-preser
 ving maps from a complete lattice to itself is a Frobenius quantale if and
  only if the lattice is completely distributive. Since completely distribu
 tive lattices are the nuclear objects in the autonomous category of comple
 te lattices and sup-preserving maps\, we study the above statement in a ca
 tegorical setting. We introduce the notion of Frobenius structure in an ar
 bitrary 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-mon
 o 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 d
 ualizing object\, if the monoid of endomorphisms of an object has a Froben
 ius structure and the monoidal unit embeds into this object as a retract\,
  then the object is nuclear.\nSlides : https://pageperso.lis-lab.fr/~cedri
 c.de-lacroix-de-lavalette/diapo/diapo_ldp_17112022.pdf \n\nL’exposé ser
 a également retransmis ici :\n\nhttps://greenlight.lal.cloud.math.cnrs.f
 r/b/lio-hdc-jef\n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 022/10/image_seminar_ldp-Cedric_de_Lacroix-From_Frobenius_structure_to_nuc
 learity-Diagram_of_the_shape-x200.png
CATEGORIES:Séminaire,Logique et Interactions
LOCATION:I2M Luminy - Ancienne BU\, Salle Séminaire2 (RdC)\, 163 Avenue de
  Luminy\, 13009 Marseille\, France\, 
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, 1300
 9 Marseille\, France\, ;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - Ancienne B
 U\, Salle Séminaire2 (RdC):geo:0,0
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