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SUMMARY:Adam-Christiaan van Roosmalen (Hasselt University\, Belgium)
DTSTART:20200715T140000Z
DTEND:20200715T150000Z
DTSTAMP:20260423T005741Z
UID:SheAlgSem/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SheAlgSem/8/
 ">Localizations of exact and one-sided exact categories.</a>\nby Adam-Chri
 stiaan van Roosmalen (Hasselt University\, Belgium) as part of Sherbrooke 
 algebra seminar\n\n\nAbstract\nQuotients of abelian and triangulated categ
 ories are ubiquitous in geometry\, representation theory\, and K-theory.  
 In recent research\, we consider quotients of exact categories by percolat
 ing subcategories.  This approach extends earlier localization theories fo
 r exact categories by Cardenas and Schlichting\, allowing new examples.\n\
 nWe obtain the quotient of an exact category E by a percolating subcategor
 y A in two steps.  In the first step\, we localize the exact category E at
  a class of morphisms S_A.  In general\, this localization need not be an 
 exact category\, but merely one-sided exact.  In the second step\, one can
  obtain the quotient E/A as the exact hull of the localization.  Furthermo
 re\, the quotient functor E --> E/A induces a Verdier localization on the 
 level of the bounded derived categories.\n\nIn this talk\, I will discuss 
 this quotient construction and briefly discuss some applications and examp
 les.\n\n(Based on joint work with Ruben Henrard.)\n
LOCATION:https://researchseminars.org/talk/SheAlgSem/8/
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