# 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} }

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…

## 2 Citations

On Diers theory of Spectrum I : Stable functors and right multi-adjoints.

- Mathematics
- 2020

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

- Mathematics
- 2019

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.

- Mathematics
- 2020

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

- Mathematics
- 2019

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

- Mathematics
- 2009

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

- Mathematics
- 2009

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

- Computer Science
- 1994

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