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

Zariski-type spectra of localic rings and monoids

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If you have a question about this talk, please contact José 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 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 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.

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