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UID:20260721T095302EDT-1067ZaA3xL@132.216.98.100
DTSTAMP:20260721T135302Z
DESCRIPTION:Some (possibly weakly) closed categories\n\nI am interested in 
 the so-called 'weak' higher dimensional categories (HDC's) as universes in
  which to do category theory\, and intuitionistic set theory as a part of 
 category theory. The adjective 'weak' refers to a type-dependent replaceme
 nt of (Fregean\, logical) equality by a 'coherence' structure. On the lowe
 st level\, this means replacing equality of sets\, and more generally\, eq
 uality of objects in a category\, by isomorphisms -- following Bourbaki an
 d Lawvere. The totally-weak HDC's\, for instance tricategories\, and more 
 generally the Batanin-type n-categories\, are ideal from a conceptual poin
 t of view\, but very difficult to work with\, or in. Therefore a coherence
  theorem\, such as the one that establishes that a certain 'semi-strict' (
 or 'semi-weak') concept called 'Gray category' is 'equivalent' to 'tricate
 gory' is a welcome excuse to concentrate on the semi-strict concept. To mo
 tivate the technical work on Gray categories\, I will show how 'weak' vers
 ions of the usual categorical concepts of pullback and discrete fibration 
 give intuitively convincing access to set-theoretic concepts such as the p
 ower-set\, differently from topos theory. To begin the mathematics of Gray
  categories\, I will define\, for Gray categories X and A\, an internal ho
 m-object [X\,A]\, itself a Gray category\, and show that it is the basis f
 or an -- at least 'weakly' -- closed structure in the sense of Eilenberg a
 nd Kelly.\n
DTSTART:20181023T183000Z
DTEND:20181023T193000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Michael Makkai\, McGill
URL:https://www.mcgill.ca/mathstat/channels/event/michael-makkai-mcgill-290
 816
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