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SUMMARY:Tomáš Jakl (Czech Academy of Sciences / Czech Technical Universi
 ty)
DTSTART:20240202T110000Z
DTEND:20240202T120000Z
DTSTAMP:20260315T014755Z
UID:TheoryCSBham/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TheoryCSBham
 /2/">Feferman–Vaught–Mostowski theorems and game comonads</a>\nby Tom
 áš Jakl (Czech Academy of Sciences / Czech Technical University) as part
  of University of Birmingham theoretical computer science seminar\n\nLectu
 re held in LG23\, Computer Science.\n\nAbstract\nIn recent years we have s
 een a growing number of examples of model\ncomparison games (such as pebbl
 e games or Ehrenfreucht-Fraisse games)\nbeing encoded semantically\, as co
 monads on the class of graphs or\nrelational structures. Apart from the co
 nnections with logic (via the\nmodel comparison games)\, game comonads can
  also express a range of\nimportant parameters in finite model theory and 
 combinatorics\, such as\ntree-width and tree-depth.\n\nAfter a brief overv
 iew of the emerging theory of game comonads\, I\nwill present my joint wor
 k with Dan Marsden and Nihil Shah. Our main\nfocus are the so-called Fefer
 man–Vaught-Mostowski-type theorems\, which\nexpress when an operation on
  models preserves equivalence in a given logic.\n\nProving these theorems 
 in the comonadic setting amounts to defining\na Kleisli law and checking c
 ertain smoothness conditions. Surprisingly\,\nthe main ingredient of our a
 pproach is a generalisation of how monoidal\nmonads lift the monoidal stru
 cture to the category of algebras.\nFurthermore\, we also show the role of
  bilinear maps in this setting and\nhow Johnstone's adjoint lifting theore
 m is a special case of all this.\n
LOCATION:https://researchseminars.org/talk/TheoryCSBham/2/
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