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DTSTAMP:20260624T060739Z
DESCRIPTION:Title: Some remarks on simplicial sets and certain related cate
 gories (continued)\n\nAbstract:\n\nIn my three-part paper 'Generalized ske
 tches as a framework for completeness theorems' (JPAA 1997)\, I construct\
 , for each of a number of categorical doctrines\, call it D\, a presheaf c
 ategory C such that D is the full subcategory of C with objects that are i
 njective relative to a small\, usually finite\, number of arrows\, the 'sk
 etch-axioms'\, in C \; the set of the sketch-axioms I denote by A . For ex
 ample\, if D is the category of small finite-limit categories (with arrows
  the functors preserving finite limits in the non-strict sense)\, than C i
 s the category (with suitable arrows!) of finite-limit sketches. In each o
 f the examples of D \, one has two weak factorization systems (the factori
 ng diagonal is not required to be unique)\, one of them giving rise\, usin
 g the above set A of 'sketch-axioms' to the objects of D as the Kan comple
 xes arise as the fibrant objects\, from the horn-extensions in the Quillen
  model structure on simplicial sets. I am interested in the question for w
 hich of my examples of sketch-categories C the two factorization systems d
 etermine a Quillen model structure\; in some simple cases\, I already know
  that this is case. In the sketch-categories\, the strict anodyne maps pla
 y a distinguished role. These are the ones that\, in the classical case of
  simplicial sets\, are obtained from the Gabriel-Zisman definition of anod
 yne map by omitting reference to retracts. In the sketch-category C\, the 
 strict anodyne maps are the transfinite composites of pushouts of the sket
 ch-axioms\, the arrows in the set A . (In the classical case also\, the st
 rict anodynes are the transfinite composites of the pushouts of the horn-e
 xtensions.) In the talk\, I will start with discussing the classical case 
 of the category of simplicial sets with a special emphasis on the strict a
 nodyne maps\, and a variant of the latter related to Andre Joyal's model s
 tructure on simplicial sets where the fibrant object are the quasi-categor
 ies\n
DTSTART:20191112T193000Z
DTEND:20191112T203000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Michael. Makkai (91ºÚÁÏÍø)
URL:/mathstat/channels/event/michael-makkai-mcgill-302
 422
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