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SUMMARY:Zariski-type spectra of localic rings and monoids - Graham Manuell
  (University of Edinburgh)
DTSTART:20191203T141500Z
DTEND:20191203T151500Z
UID:TALK135541@talks.cam.ac.uk
CONTACT:José Siqueira
DESCRIPTION:The Zariski spectrum provides a way to associate a topological
  space (or better\, a locale) to a commutative ring. Similar spectrum cons
 tructions include the Gelfand spectrum of a C*-algebra\, the Stone spectru
 m of a bounded distributive lattice and the Hofmann–Lawson spectrum of a
  distributive continuous lattice. Generalising these examples\, we define 
 a notion of spectrum of a commutative localic semiring via a universal pro
 perty. Furthermore\, we define a quantalic spectrum which generalises the 
 quantale of ideals of a ring and from which the localic spectrum can be re
 covered. By leveraging dualisable objects in the monoidal category of supl
 attices\, we describe an explicit construction of this spectrum (under cer
 tain conditions) and an analogous spectrum of commutative localic monoids.
LOCATION:MR4\, Centre for Mathematical Sciences
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