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.
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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.
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