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Mathematics 2017, 5(3), 37; doi:10.3390/math5030037

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)
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Abstract

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).

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Tuyéras, R. Elimination of Quotients in Various Localisations of Premodels into Models. Mathematics 2017, 5, 37.

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