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SUMMARY:Luisa Fiorot
DTSTART:20210305T153000Z
DTEND:20210305T160000Z
DTSTAMP:20260421T120749Z
UID:cats2021/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/cats2021/21/
 ">n-quasi-abelian categories</a>\nby Luisa Fiorot as part of Additive cate
 gories between algebra and functional analysis\n\n\nAbstract\nGiven an abe
 lian category A its derived category D(A) admits a natural t-structure who
 se heart is A. Moreover by the Auslander’s Formula A is equivalent to th
 e quotient category of coherent functors by the Serre subcategory of effec
 able functors.\n\nWe can associate to an exact category E  its derived cat
 egory D(E)\, does D(E) admit a canonical t-structure? If such a t-structur
 e exists\, is it possible to describe its heart in terms of coherent funct
 ors?\n\nTesting this problem on a quasi-abelian category E we get:\nits de
 rived category D(E) admits two canonical t-structures (left and right) who
 se hearts L and R are derived equivalent and their intersection in D(E) is
  E.\nIf E is quasi-abelian but not abelian the "distance" between these tw
 o t-structures is 1\, while in the abelian\ncase these two t-structures co
 incides and their "distance" is 0.\nMoreover L (resp. R) can be described 
 by the Auslander’s Formula as the quotient category of contravariant (re
 sp. covariant) coherent functors by the Serre subcategory of effecable fun
 ctors.\n\nWe extend this picture into a hierarchy of n-quasi-abelian categ
 ories: n=0 are abelian categories\, n=1 are quasi-abelian categories\, n=2
  are pre-abelian categories....\n\n\nThis talk is based on the paper\nhttp
 s://arxiv.org/abs/1602.08253v3\n
LOCATION:https://researchseminars.org/talk/cats2021/21/
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