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BEGIN:VEVENT
UID:/NewsandEvents/Events/Upcoming-Events/newsitem
/10145/12-September-2018-Algebra|Coalgebra-Seminar
-Ganna-Kudryavtseva
DTSTAMP:20180905T022526
SUMMARY:Algebra|Coalgebra Seminar, Ganna Kudryavts
eva
ATTENDEE;ROLE=Speaker:Ganna Kudryavtseva (Universi
ty of Ljubljana)
DTSTART:20180912T160000
DTEND: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 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.

\n\n The talk is based on a
joint work with Mark V. Lawson.

\n
URL:http://events.illc.uva.nl/alg-coalg
CONTACT:Frederik Lauridsen at f.m.lauridsen at uva
.nl
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