Elimination of Quotients in Various Localisations of Premodels into Models
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...
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doaj-785bdedca9df4c048cf940c4fe75fd0f2020-11-25T00:38:15ZengMDPI AGMathematics2227-73902017-07-01533710.3390/math5030037math5030037Elimination of Quotients in Various Localisations of Premodels into ModelsRémy Tuyéras0Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USAThe 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.https://www.mdpi.com/2227-7390/5/3/37algebraic objectsquotientssmall object argument |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Rémy Tuyéras |
spellingShingle |
Rémy Tuyéras Elimination of Quotients in Various Localisations of Premodels into Models Mathematics algebraic objects quotients small object argument |
author_facet |
Rémy Tuyéras |
author_sort |
Rémy Tuyéras |
title |
Elimination of Quotients in Various Localisations of Premodels into Models |
title_short |
Elimination of Quotients in Various Localisations of Premodels into Models |
title_full |
Elimination of Quotients in Various Localisations of Premodels into Models |
title_fullStr |
Elimination of Quotients in Various Localisations of Premodels into Models |
title_full_unstemmed |
Elimination of Quotients in Various Localisations of Premodels into Models |
title_sort |
elimination of quotients in various localisations of premodels into models |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2017-07-01 |
description |
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. |
topic |
algebraic objects quotients small object argument |
url |
https://www.mdpi.com/2227-7390/5/3/37 |
work_keys_str_mv |
AT remytuyeras eliminationofquotientsinvariouslocalisationsofpremodelsintomodels |
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1725298206334517248 |