Elimination of Quotients in Various Localisations of Premodels into Models
Author(s)Tuyeras, Remy V
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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-categories, weak ω-groupoids and higher moduli stacks.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Tuyéras, Rémy. "Elimination of Quotients in Various Localisations of Premodels into Models." Mathematics 5, 3 (July 2017): 37 © 2017 The Author
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