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University of Cambridge > Talks.cam > Category Theory Seminar > Zariski-type spectra of localic rings and monoids

## Zariski-type spectra of localic rings and monoidsAdd to your list(s) Download to your calendar using vCal - Graham Manuell (University of Edinburgh)
- Tuesday 03 December 2019, 14:15-15:15
- MR4, Centre for Mathematical Sciences.
If you have a question about this talk, please contact JosĂ© Siqueira. The Zariski spectrum provides a way to associate a topological space (or better, a locale) to a commutative ring. Similar spectrum constructions include the Gelfand spectrum of a C*-algebra, the Stone spectrum of a bounded distributive lattice and the Hofmannâ€“Lawson spectrum of a distributive continuous lattice. Generalising these examples, we define a notion of spectrum of a commutative localic semiring via a universal property. Furthermore, we define a quantalic spectrum which generalises the quantale of ideals of a ring and from which the localic spectrum can be recovered. By leveraging dualisable objects in the monoidal category of suplattices, we describe an explicit construction of this spectrum (under certain conditions) and an analogous spectrum of commutative localic monoids. This talk is part of the Category Theory Seminar series. ## This talk is included in these lists:- All CMS events
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