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SUMMARY:String diagrams for semistrict n-categories - Manuel Araujo\, Univ
 ersity of Cambridge
DTSTART:20221202T140000Z
DTEND:20221202T150000Z
UID:TALK192614@talks.cam.ac.uk
CONTACT:Jamie Vicary
DESCRIPTION:String diagrams are a powerful computational tool\, most commo
 nly used in the context of monoidal categories and bicategories. I will ta
 lk about extending this to higher dimensions. The natural setting for n-di
 mensional string diagrams should be some form of semistrict n-category\, w
 here composition operations\, corresponding to stacking of diagrams\, are 
 strictly associative and unital\, but the interchange laws hold only up to
  coherent equivalence. The idea is to define a semistrict n-category as so
 mething which admits composites for labeled string diagrams. The first ste
 p is to develop a theory of n-sesquicategories. These encode only the comp
 ositional structure of string diagrams\, without interchange laws. I will 
 explain how to define these as algebras over a monad whose operations are 
 simple string diagrams and how a theory of normal forms for the terms of t
 he associated computads leads to a proof that the category of computads is
  a presheaf category. The second step\, which is still work in progress\, 
 is to add operations implementing weak versions of the interchange laws\, 
 obtaining the desired notion of semistrict n-category. In dimension 3\, th
 is recovers the notion of Gray 3-category.
LOCATION:SS03
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