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UID:20260713T232619EDT-2037Z9Vhf5@132.216.98.100
DTSTAMP:20260714T032619Z
DESCRIPTION:Some (possibly weakly) closed categories part 2\n\nI am interes
 ted in the so-called 'weak' higher dimensional categories (HDC's) as unive
 rses in which to do category theory\, and intuitionistic set theory as a p
 art of category theory. The adjective 'weak' refers to a type-dependent re
 placement of (Fregean\, logical) equality by a 'coherence' structure. On t
 he lowest level\, this means replacing equality of sets\, and more general
 ly\, equality of objects in a category\, by isomorphisms -- following Bour
 baki and Lawvere. The totally-weak HDC's\, for instance tricategories\, an
 d more generally the Batanin-type n-categories\, are ideal from a conceptu
 al point of view\, but very difficult to work with\, or in. Therefore a co
 herence theorem\, such as the one that establishes that a certain 'semi-st
 rict' (or 'semi-weak') concept called 'Gray category' is 'equivalent' to '
 tricategory' is a welcome excuse to concentrate on the semi-strict concept
 . To motivate the technical work on Gray categories\, I will show how 'wea
 k' versions of the usual categorical concepts of pullback and discrete fib
 ration give intuitively convincing access to set-theoretic concepts such a
 s the power-set\, differently from topos theory. To begin the mathematics 
 of Gray categories\, I will define\, for Gray categories X and A\, an inte
 rnal hom-object [X\,A]\, itself a Gray category\, and show that it is the 
 basis for an -- at least 'weakly' -- closed structure in the sense of Eile
 nberg and Kelly.\n
DTSTART:20181030T183000Z
DTEND:20181030T193000Z
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-291
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