Elimination of Quotients in Various Localisations of Premodels into Models

Rémy Tuyéras
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Rémy Tuyéras: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

Mathematics, 2017, vol. 5, issue 3, 1-72

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/ ? -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 ( ? , n ) -categories, weak ? -groupoids and higher moduli stacks.

Keywords: algebraic objects; quotients; small object argument (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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