• Corpus ID: 227255005

On Diers theory of Spectrum II Geometries and dualities

@article{Osmond2020OnDT,
  title={On Diers theory of Spectrum II Geometries and dualities},
  author={Axel Osmond},
  journal={arXiv: Category Theory},
  year={2020}
}
  • Axel Osmond
  • Published 3 December 2020
  • Mathematics
  • arXiv: Category Theory
This second part comes to the construction of the spectrum associated to a situation of multi-adjunction. Exploiting a geometric understanding of its multi-versal property, the spectrum of an object is obtained as the spaces of local unit equipped with a topology provided by orthogonality aspects. After recalling Diers original construction, this paper introduces new material. First we explain how the situation of multi-adjunction can be corrected in a situation of adjunction between categories… 
On Diers theory of Spectrum I : Stable functors and right multi-adjoints.
Diers developed a general theory of right multiadjoint functors leading to a purely cate-gorical, point-set construction of spectra. Situations of multiversal properties return sets ofcanonical
The general construction of Spectra
We provide a synthesis of different topos-theoretical approaches of the general construction of spectra, exploring jointly its purely categorical, model theoretic and geometric aspects. We detail

References

SHOWING 1-10 OF 14 REFERENCES
On Diers theory of Spectrum I : Stable functors and right multi-adjoints.
Diers developed a general theory of right multiadjoint functors leading to a purely cate-gorical, point-set construction of spectra. Situations of multiversal properties return sets ofcanonical
The general construction of Spectra
We provide a synthesis of different topos-theoretical approaches of the general construction of spectra, exploring jointly its purely categorical, model theoretic and geometric aspects. We detail
Grothendieck topologies from unique factorisation systems
This work presents a way to associate a Grothendieck site structure to a (locally presentable) category endowed with a unique factorisation system of its arrows. In particular this recovers the
Derived Algebraic Geometry V: Structured Spaces
In this paper, we describe a general theory of "spaces with structure sheaves." Specializations of this theory include the classical theory of schemes, the theory of Deligne-Mumford stacks, and their
The bicategory of topoi and spectra
  • Reprints in Theory and Applications of Categories
  • 2016
Ionads
  • Special Issue devoted to the International Conference in Category Theory 'CT2010
  • 2012
Ionads”. In: Journal of Pure and Applied Algebra
  • issn: 0022-4049.doi: https://doi.org/10.1016/j.jpaa.2012.02.013. url: http://www.sciencedirect.com/science/article/pii/S0022404912000527
  • 2012
The Trace Factorisation of Stable Functors
  • url: http://www.paultaylor.eu/stable/trafsf.pdf
  • 1998
Handbook of Categorical Algebra
The Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic of
Handbook of categorical algebra: volume 1, Basic category theory
  • 1994
...
1
2
...