Next Article in Journal
Lattices and Rational Points
Previous Article in Journal
Banach Subspaces of Continuous Functions Possessing Schauder Bases
Previous Article in Special Issue
Cohen Macaulayness and Arithmetical Rank of Generalized Theta Graphs
Article Menu
Issue 3 (September) cover image

Export Article

Open AccessArticle
Mathematics 2017, 5(3), 37;

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
(This article belongs to the Special Issue Homological and Homotopical Algebra and Category Theory)
Full-Text   |   PDF [731 KB, uploaded 14 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/ Ω -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 ( ω , n ) -categories, weak ω -groupoids and higher moduli stacks. View Full-Text
Keywords: algebraic objects; quotients; small object argument algebraic objects; quotients; small object argument
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.

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.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top