Elimination of Quotients in Various Localisations of Premodels into Models
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
Academic Editor: Hvedri Inassaridze
Received: 27 March 2016 / Revised: 29 June 2017 / Accepted: 3 July 2017 / Published: 9 July 2017
The contribution of this article is quadruple. It (1) unifies various schemes of premodels/models including situations such as presheaves/sheaves, sheaves/flabby sheaves, prespectra/
-spectra, simplicial topological spaces/(complete) Segal spaces, pre-localised rings/localised rings, functors in categories/strong stacks and, to some extent, functors from a limit sketch to a model category versus the homotopical models for the limit sketch; (2) provides a general construction from the premodels to the models; (3) proposes technics that allow one to assess the nature of the universal properties associated with this construction; (4) shows that the obtained localisation admits a particular presentation, which organises the structural and relational information into bundles of data. This presentation is obtained via a process called an elimination of quotients
and its aim is to facilitate the handling of the relational information appearing in the construction of higher dimensional objects such as weak
-groupoids and higher moduli stacks.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
Tuyéras, R. Elimination of Quotients in Various Localisations of Premodels into Models. Mathematics 2017, 5, 37.
Tuyéras R. Elimination of Quotients in Various Localisations of Premodels into Models. Mathematics. 2017; 5(3):37.
Tuyéras, Rémy. 2017. "Elimination of Quotients in Various Localisations of Premodels into Models." Mathematics 5, no. 3: 37.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
For more information on the journal statistics, click here
Multiple requests from the same IP address are counted as one view.