Publication

Filter quotients and non-presentable (∞,1)-toposes

Nima Rasekh
2021
Journal Articles

Abstract

We define filter quotients of -categories and prove that filter quotients preserve the structure of an elementary -topos and in particular lift the filter quotient of the underlying elementary topos. We then specialize to the case of filter products of -categories and prove a characterization theorem for equivalences in a filter product. Then we use filter products to construct a large class of elementary -toposes that are not Grothendieck -toposes. Moreover, we give one detailed example for the interested reader who would like to see how we can construct such an -category, but would prefer to avoid the technicalities regarding filters.

Official source

https://infoscience.epfl.ch/entities/publication/35a78646-e874-422d-813c-b3aa9ab54238

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Nima Rasekh
2021
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/35a78646-e874-422d-813c-b3aa9ab54238

About this result

Related concepts (32)

Filters in topology

Filters in topology, a subfield of mathematics, can be used to study topological spaces and define all basic topological notions such as convergence, continuity, compactness, and more. Filters, which are special families of subsets of some given set, also provide a common framework for defining various types of limits of functions such as limits from the left/right, to infinity, to a point or a set, and many others. Special types of filters called have many useful technical properties and they may often be used in place of arbitrary filters.

Topos

In mathematics, a topos (USˈtɒpɒs, UKˈtoʊpoʊs,_ˈtoʊpɒs; plural topoi ˈtɒpɔɪ or ˈtoʊpɔɪ, or toposes) is a that behaves like the category of sheaves of sets on a topological space (or more generally: on a site). Topoi behave much like the and possess a notion of localization; they are a direct generalization of point-set topology. The Grothendieck topoi find applications in algebraic geometry; the more general elementary topoi are used in logic. The mathematical field that studies topoi is called topos theory.

Quasi-category

In mathematics, more specifically , a quasi-category (also called quasicategory, weak Kan complex, inner Kan complex, infinity category, ∞-category, Boardman complex, quategory) is a generalization of the notion of a . The study of such generalizations is known as . Quasi-categories were introduced by . André Joyal has much advanced the study of quasi-categories showing that most of the usual basic and some of the advanced notions and theorems have their analogues for quasi-categories.

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