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SUMMARY:Mark Kamsma
DTSTART:20251009T130000Z
DTEND:20251009T140000Z
DTSTAMP:20260421T154347Z
UID:UEAPS/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UEAPS/58/">C
 ofibrant generation of pure monomorphisms in presheaf categories</a>\nby M
 ark Kamsma as part of ANTLR seminar\n\n\nAbstract\nThe title of this talk\
 , and its main result\, are purely category-theoretic. However\, we use mo
 del-theoretic methods to obtain the result. For a fixed monoid $S$\, there
  is an algebraic question whether or not pure monomorphisms between sets w
 ith an $S$-action are cofibrantly generated. In (positive) model theory\, 
 we sometimes call pure monomorphisms immersions: those homomorphisms that 
 reflect solutions to systems of equations. An earlier result by Lieberman\
 , Vasey and Rosický established an equivalence between the existence of a
  stable independence relation on a category and cofibrant generation of a 
 certain class of morphisms. We use this equivalence\, as well as ideas of 
 Mustafin\, to characterise for which monoids $S$ the class of pure monomor
 phisms is cofibrantly generated: those such that for every $a\, b \\in S$ 
 there is $c \\in S$ with $a = cb$ or $b = ca$. Our methods directly go thr
 ough in the greater generality of presheaf categories\, hence the title\, 
 and main result\, of the talk.\n\nThis is joint work with Sean Cox\, Jonat
 han Feigert\, Marcos Mazari-Armida and Jiří Rosický.\n
LOCATION:https://researchseminars.org/talk/UEAPS/58/
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