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CATEGORIES:Theoretical computer science seminar
SUMMARY:Geometric morphisms as structure preserving maps a
nd other nice characterisations - Christopher Town
send
DTSTART:20190607T093000Z
DTEND:20190607T110000Z
UID:TALK3775AT
URL:/talk/index/3775
DESCRIPTION:Geometric morphisms\, the 'correct' arrows between
toposes\,\ncan be represented as adjunctions betw
een categories of locales over\ntoposes. Categorie
s of locales can be axiomatised using the double p
ower\nlocale monad\, so it is pleasing to note tha
t the adjunctions\ncorresponding to geometric morp
hisms are those that commute with the\ndouble powe
r locale monad\; i.e. structure preserving maps. T
he talk will\nfurther explore the many different a
dditional ways that these\nadjunctions between cat
egories of locales can be characterised. We will\n
prove\, in reasonable detail\, an omnibus theorem
showing that geometric\nmorphisms can also be char
acterised as:\n\n1.Frobenius adjunctions\n\n2.Stab
ly Frobenius adjunctions\n\n3.Upper and lower powe
r locale monad preserving adjunctions\n\n4.Hilsum-
Skandalis maps\n\n5.The connected components adjun
ction of an internal groupoid\n\nThe talk will ass
ume familiarity with topos theory and locale theor
y.\n
LOCATION:Computer Science\, The Sloman Lounge (UG)
CONTACT:Benedikt Ahrens
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