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SUMMARY:Layered monoidal theories - Leo Lobski (University College London)
DTSTART:20260227T140000Z
DTEND:20260227T150000Z
UID:TALK244828@talks.cam.ac.uk
DESCRIPTION:Systems across science and engineering naturally arrange into 
 levels of abstraction: reaction networks treat chemical compounds as place
 holders with no internal structure\, whereas the molecular structure is co
 nsidered when modelling the compounds as graphs\; the molecular structure 
 can further be seen as an abstraction of quantum chemical models\; similar
 ly\, higher level descriptions in computer architecture must ultimately be
  implemented as microelectronic circuits.\n\nIn this talk\, I will introdu
 ce layered monoidal theories as a mathematical framework for studying the 
 levels of abstraction. While monoidal theories provide a well-developed an
 d intuitive graphical syntax for many scientific theories via their repres
 entation as string diagrams\, they lack a uniform way of incorporating tra
 nslations between theories. Categorical models\, therefore\, deal with tra
 nslations – such as adjunctions or functors refining a more abstract the
 ory by translating it to a more detailed one – on a case-by-case basis. 
 Layered monoidal theories remedy this by "glueing together" several monoid
 al theories as well as translations between them\, while retaining the rec
 ursively defined syntax and semantic interpretability. After defining laye
 red monoidal theories\, I will demonstrate how they can be used to reason 
 about various systems via three examples: digital circuits\, electrical ci
 rcuits and chemical reactions.
LOCATION:SS03\, Computer Laboratory
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