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SUMMARY:Ivo Herzog (Ohio State University\, USA)
DTSTART:20210525T160000Z
DTEND:20210525T170000Z
DTSTAMP:20260423T021247Z
UID:ONCAS/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ONCAS/5/">Th
 e Positselski-Štovíček Correspondence for the Recollements of Purity</a
 >\nby Ivo Herzog (Ohio State University\, USA) as part of ONCAS Online Non
 commutative Algebra Seminar\n\n\nAbstract\nThe theory of purity for module
 s over a ring R has been studied using the covariant\nas well as the contr
 avariant functor categories. In their work on quiver Grassmanians\,\nCrawl
 ey-Boevey and Sauter introduced a third such category\, the projective quo
 tient \nfunctor category. We will explain how these three functor categori
 es are related to the three equivalent definitions of purity. Ironically\,
  the projective quotient functor category is closest in spirit to Prüfer'
 s original definition. \n\nEach of these functor categories may be regarde
 d as the middle term of a recollement of abelian categories whose localiza
 tion/colocalization is given by the category R-Mod of R-modules. We will d
 escribe the basic theory of recollements of functor categories and indicat
 e how it reveals the common features of the three functor categories. Each
  of these functor categories is related to the other two by a triangle of 
 Positselski-Štovíček correspondences\, which allows a detailed analysis
  of its homological properties. \n\nThis is joint work with Xianhui Fu.\n
LOCATION:https://researchseminars.org/talk/ONCAS/5/
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