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SUMMARY:Henrik Holm (University of Copenhagen\, Denmark)
DTSTART:20220426T160000Z
DTEND:20220426T170000Z
DTSTAMP:20260423T021408Z
UID:ONCAS/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ONCAS/17/">T
 he Q-shaped derived category of a ring</a>\nby Henrik Holm (University of 
 Copenhagen\, Denmark) as part of ONCAS Online Noncommutative Algebra Semin
 ar\n\n\nAbstract\nThe derived category D(A) of the category Mod(A) of modu
 les over a ring A is an important example of a triangulated category in al
 gebra. It can be obtained as the homotopy category of the category Ch(A) o
 f chain complexes of A-modules equipped with its standard model structure.
  One can view Ch(A) as the category Fun(Q\,Mod(A)) of additive functors fr
 om a certain small preadditive category Q to Mod(A). The model structure o
 n Ch(A) = Fun(Q\,Mod(A)) is not inherited from a model structure on Mod(A)
  but arises instead from the "self-injectivity" of the special category Q.
  We will show that the functor category Fun(Q\,Mod(A)) has two interesting
  model structures for many other self-injective small preadditive categori
 es Q. These two model structures have the same weak equivalences\, and the
  associated homotopy category is what we call the Q-shaped derived categor
 y of A. We will also show that it is possible to generalize the homology f
 unctors on Ch(A) to homology functors on Fun(Q\,Mod(A)) for most self-inje
 ctive small preadditive categories Q. The talk is based on a joint paper w
 ith Peter Jørgensen (arXiv:2101.06176)\, which has the same title as the 
 talk.\n
LOCATION:https://researchseminars.org/talk/ONCAS/17/
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