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SUMMARY:Another viewpoint on cartesian theories - Zhen Lin Low (University
  of Cambridge)
DTSTART:20151124T141500Z
DTEND:20151124T151500Z
UID:TALK62688@talks.cam.ac.uk
CONTACT:Dr Ignacio Lopez Franco
DESCRIPTION:As is well known\, cartesian theories have essentially the sam
 e expressive\npower as finite limit sketches\, but some details are lost i
 n the\ntranslation: for instance\, a cartesian theory has an underlying al
 gebraic\ntheory\, but this disappears after passing to the syntactic categ
 ory. The\ngap can be bridged by introducing the notion of cartesian hyperd
 octrine.\nSuch a structure gives rise to a category of fibrant objects\, a
 nd in the\ncase of the cartesian hyperdoctrine generated by a cartesian th
 eory T\, its\nhomotopy category is the syntactic category of T. The same c
 onstruction\nalso specialises to yield the reg/lex completion and the cate
 gory of\nassemblies for a pca.
LOCATION:MR5\, Centre for Mathematical Sciences
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