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UID:/NewsandEvents/Archives/2018/newsitem/10145/12
 -September-2018-Algebra|Coalgebra-Seminar-Ganna-Ku
 dryavtseva
DTSTAMP:20180905T022526
SUMMARY:Algebra|Coalgebra Seminar, Ganna Kudryavts
 eva
ATTENDEE;ROLE=Speaker:Ganna Kudryavtseva (Universi
 ty of Ljubljana)
DTSTART;TZID=Europe/Amsterdam:20180912T160000
DTEND;TZID=Europe/Amsterdam:20180912T170000
LOCATION:Room F3.20, KdV, Science Park 107, Amster
 dam
DESCRIPTION:We discuss an extension of fundamental
  results of frame theory to a non-commutative sett
 ing where the role of locales is taken over by eta
 le localic categories. These categories are put in
  a duality with complete and infinitely distributi
 ve restriction monoids (restriction monoids being 
 a well-established class of non-regular generaliza
 tions of inverse monoids). As a special case this 
 includes the duality between etale localic groupoi
 ds and pseudogroups (defined as complete and infin
 itely distributive inverse monoids). The relations
 hip between categories and monoids is mediated by 
 a class of quantales called restriction quantal fr
 ames. Projecting down to topological setting, we e
 xtend the classical adjunction between locales and
  topological spaces to an adjunction between etale
  localic categories and etale topological categori
 es. As a consequence, we deduce a duality between 
 distributive restriction semigroups and spectral e
 tale topological categories. Our work unifies and 
 upgrades the earlier work by Pedro Resende, and al
 so by Mark V. Lawson and Daniel H. Lenz.  The talk
  is based on a joint work with Mark V. Lawson.
X-ALT-DESC;FMTTYPE=text/html:\n  <p>We discuss an 
 extension of fundamental results of frame theory t
 o a non-commutative setting where the role of loca
 les is taken over by etale localic categories. The
 se categories are put in a duality with complete a
 nd infinitely distributive restriction monoids (re
 striction monoids being a well-established class o
 f non-regular generalizations of inverse monoids).
  As a special case this includes the duality betwe
 en etale localic groupoids and pseudogroups (defin
 ed as complete and infinitely distributive inverse
  monoids). The relationship between categories and
  monoids is mediated by a class of quantales calle
 d restriction quantal frames. Projecting down to t
 opological setting, we extend the classical adjunc
 tion between locales and topological spaces to an 
 adjunction between etale localic categories and et
 ale topological categories. As a consequence, we d
 educe a duality between distributive restriction s
 emigroups and spectral etale topological categorie
 s. Our work unifies and upgrades the earlier work 
 by Pedro Resende, and also by Mark V. Lawson and D
 aniel H. Lenz.</p>\n\n  <p>The talk is based on a 
 joint work with Mark V. Lawson.</p>\n
URL:http://events.illc.uva.nl/alg-coalg
CONTACT:Frederik Lauridsen at f.m.lauridsen at uva
 .nl
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