Elimination of Quotients in Various Localisations of Premodels into Models
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mathematics-05-00037-v2.pdf
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731.39 KB
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f55472a6653b0170e7f72a6fde804cbd
Author(s)
Tuyeras, Remy V
Date Issued
July 2017
Journal
Mathematics
Publisher
MDPI AG
Citation
Tuyéras, Rémy. "Elimination of Quotients in Various Localisations of Premodels into Models." Mathematics 5, 3 (July 2017): 37 © 2017 The Author
Version
Final published version
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-categories, weak ω-groupoids and higher moduli stacks.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.3390/math5030037
