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SUMMARY:Constructing monoidal theories with open-graphs and rewrite catego
 ries - Aleks Kissinger\, University of Oxford
DTSTART:20110524T131500Z
DTEND:20110524T144500Z
UID:TALK31577@talks.cam.ac.uk
CONTACT:Nathan Bowler
DESCRIPTION:In this talk\, I'll define open-graphs\, which are special kin
 ds of typed directed graphs that are well suiting for constructing free mo
 noidal categories. These are best thought of as discretisations of polaris
 ed topological graphs\, which Joyal and Street used to formalise graphical
  languages for monoidal categories in 1991. As in topological graphs\, edg
 es in open-graphs can be disconnected at one or both ends (forming inputs 
 and outputs) and can be connected to themselves (forming circles). However
 \, unlike topological graphs\, open-graphs are discete\, finitary\, and we
 ll-suited to computational applications using existing techniques in graph
  rewriting. I'll discuss how rewriting can be performed using the "double 
 pushout" technique in the ambient adhesive category of typed graphs and sh
 ow how open-graphs modulo certain rewrite systems can be used to construct
  free monoidal categories\, PROPs\, and more general monoidal theories. If
  there is time\, I'll discuss how we are applying these techniques to the 
 study\nof many-body quantum entanglement.
LOCATION:MR3\, Centre for Mathematical Sciences
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