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SUMMARY:Unfinity Categories - Andrew Pitts\, University of Cambridge
DTSTART:20210326T140000Z
DTEND:20210326T150000Z
UID:TALK158236@talks.cam.ac.uk
CONTACT:Jamie Vicary
DESCRIPTION:https://us02web.zoom.us/j/177472153?pwd=MFgwd0EzY05QSGtpSDc2dU
 16aG9wdz09\n\nThere is a nominal approach to higher dimensional structure 
 using sets\nwhose elements are supported by finite subsets of an "unfinite
 " set of\nnamed dimensions (x-axis\, y-axis\, z-axis\, etc.)\, modulo perm
 utation\nsymmetry of the named dimensions. For example\, an element whose\
 nsupport is {x\,y\,z} has dimenion 3. By considering such sets equipped\nw
 ith a simple notion of end-point (0/1) substitution\, one arrives at a\nca
 tegory equivalent to the category of cubical sets (with name\nabstraction 
 corresponding to path objects) that is the starting point\nfor the Bezem-C
 oquand-Huber model of homotopy type theory (HoTT). (See\nPitts\, Proc. TYP
 ES 2014.)\n\nI will sketch these ideas and then show how strict cubical\no
 mega-categories can be defined quite simply in this style (using the\nform
 ulation of "category" in which objects are identified with\nidentity morph
 isms). I will also speculate why this might be\ninteresting from the point
  of view of models of HoTT.
LOCATION:Online
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