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Suppose is a functor that has a left multiadjoint.
The Diers spectrum of is the functor that sends an object to the set that indexes the value of the left multiadjoint of at . A morphism is sent to the induced map that assigns to the unique such that factors through .
The category of integral domains and injective homomorphisms is a multireflexive subcategory of the category of commutative rings and ring homomorphisms.
The associated Diers spectrum functor is a functor
that sends a commutative ring to its prime spectrum.
The category of reduced rings and injective homomorphisms is a multireflexive subcategory of the category of commutative rings and ring homomorphisms.
The associated Diers spectrum functor is a functor
that sends a commutative ring to its poset of radical ideals. This is precisely the underlying poset of the localic Zariski spectrum?.
Yves Diers, Some spectra relative to functors. Journal of Pure and Applied Algebra 22:1 (1981), 57–74. doi
Axel Osmond: On Diers theory of Spectrum I: Stable functors and right multi-adjoints, arXiv.
Axel Osmond: On Diers theory of Spectrum II Geometries and dualities, arXiv.
Last revised on April 8, 2021 at 18:36:44. See the history of this page for a list of all contributions to it.