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SUMMARY:Sinem Odabaşı (Universidad Austral de Chile)
DTSTART:20210217T150000Z
DTEND:20210217T160000Z
DTSTAMP:20260422T172357Z
UID:UCGEN/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCGEN/27/">O
 n induced cotorsion pairs in functor category.</a>\nby Sinem Odabaşı (Un
 iversidad Austral de Chile) as part of UCGEN - Uluslararası Cebirsel GEom
 etri Neşesi\n\n\nAbstract\nThe question of interest that motivates our wo
 rk is how to ensure that the category Add (A\,R-Mod) of additive functors 
 has a projective / injective model structure without putting any condition
 s on the ring R. Essentially\, it is motivated by the classical projective
 /injective/flat model structures on the category Ch(R) of chain complexes 
 of left R-modules.\n\n While we have been working on this problem with my 
 collegues\, in a recent work of Henrik Holm and Peter Jorgensen published 
 in arXiv arXiv:2101.06176\, this problem is handled by using techniques/re
 sults in Gorenstein Homological Algebra. \n\nFortunately\, our approach di
 ffers from theirs\, and includes other contexts such as module category ov
 er a formal triangular matrix ring.\n\nWith this objective in mind\, in th
 is talk we will talk about how to build "possible" Hovey cotorsion pairs^1
  in Add (A\, R-Mod)\, and later we will present an explicit characterizati
 on of their objects. The results obtained on these cotorsion pairs in Add 
 (A\, R-Mod) generalize the known results in the categories of chain comple
 xes of R-modules and modules over a formal triangular matrix ring. It is a
  work in progress with Sergio Estrada and Manuel Cortes Izurdiaga.\n\n1: T
 here is a close relation between abelian model structures in abelian categ
 ories and Hovey pairs\; see [Hov02]. That's why we focus on finding suitab
 le Hovey pairs in Add (A\, R-Mod).\n\n[Hov02] Hovey\, M. Cotorsion pairs\,
  model category structures\, and representation theory. Math Z 241\, 553
 –592 (2002).\n
LOCATION:https://researchseminars.org/talk/UCGEN/27/
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