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UID:6590@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20210107T103000
DTEND;TZID=Europe/Paris:20210107T113000
DTSTAMP:20241120T201748Z
URL:https://www.i2m.univ-amu.fr/evenements/the-bicategory-of-open-functors
 -and-its-friends-luidnel-maignan-4/
SUMMARY:Luidnel Maignan (LACL\, UPEC\, Créteil): The Bicategory of “Open
  Functors” and its Friends – Luidnel Maignan
DESCRIPTION:Luidnel Maignan: We want to replace categories\, functors and n
 atural transformations by categories\, open functors and open natural tran
 sformations. The adjective open is added here to mean that some external i
 nformation is taken into account. The origin of this will is that we neede
 d to generalize the powerset monad in a setting where sets are replaced by
  categories in our on so-called global transformations\, in order to handl
 e non-determinism.\nThe first tries was to replace objects by sets of obje
 cts and morphisms by some sort of sets of morphisms. However\, we found co
 nvincing examples to think that multiplicities was important\, and multipl
 icities came from the different ways a result could be obtained.\nSo to ta
 ke into account the multiplicities was the same as to tag  »each output 
 with the reason » of its occurrence. These « reasons » form our exte
 rnal information.\nAll in all\, this information can be viewed as the resu
 lt of a choice\, either from a random source\, from an external scheduler\
 , or simply from another part of the system that is not modeled but just t
 aken as secondary input instead (e.g. Field-Based Cellular Automata\,\nRan
 dom Cellular Automata). Although it seemed clear that some settings should
  already exist\, there were questions on small details in each possible se
 tting. In such a case\, it is a good idea to first formalize the intuition
  as it is\, and then try afterward to map it in other settings in a precis
 e formal way to fix those details. This is exactly the purpose of this pap
 er: to formelize open functors directly\, and then see how presheaves\, mo
 nads\, fibrations\, and distributors (also called profunctors) show up or 
 compare.\nThis is a work in progress with Alexandre Fernandez and Antoine 
 Spicher.
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Luidnel_Maignan.jpg
CATEGORIES:Séminaire,Logique et Interactions,Virtual event
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