2015/11/30 by Rémy Tuyéras
Mathematics · #Algebra over a field #Algorithm #Functor #Homotopy #Homotopy and Cohomology in Algebraic Topology #Limit (mathematics) #Linguistics #Mathematical analysis #Mathematics #Model category #Omega #Pure mathematics #Quotient #Representation (politics) #Sketch #math.AG #math.CT #math.KT
paper · pdf · doi:10.3390/math5030037
published as Mathematics, 5(3), 37, (2017) · The text is the same as in v6; this version contains corrections to the published MDPI paper, the main reason for this change is that the diagram of Proposition 3.1 was meant to be a 3 dimensional diagram (while only the front face appeared in the published paper). The wording of some sentences and the diagram of Example 6.42 are changed accordingly. A typo in the table of Ex. 6.42 is corrected
openalex created_date 2016/06/24 · openalex publication_date 2017/07/09 · arxiv created 2017/09/12 · arxiv updated 2017/09/13 · openalex updated_date 2026/08/05
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.