5 citations · 9 across the 9 of their papers we have counts for
15 papers
The smallest -pure subtopos and dimension theory
Jens Hemelaer
We introduce the notion of -pure geometric morphism between Grothendieck toposes, over a Grothendieck base topos . This is a higher-dimensional analogue of the conc…
Localization of monoids and topos theory
Jens Hemelaer
Let be a monoid that is embeddable in a group. We consider the topos of sets equipped with a right -action, and we study the subtoposes that are of monoid…
Toposes over which essential implies locally connected
Jens Hemelaer
We introduce the notion of an EILC topos: a topos such that every essential geometric morphism with codomain is locally connected. We then show that the…
Geometric morphisms between toposes of monoid actions: factorization systems
Jens Hemelaer, Morgan Rogers
Let M, N be monoids, and PSh(M), PSh(N) their respective categories of right actions on sets. In this paper, we systematically investigate correspondences between properties of geo…
Solution to a problem by FitzGerald
Jens Hemelaer, Morgan Rogers
FitzGerald identified four conditions (RI), (UR), (RI*) and (UR*) that are necessarily satisfied by an algebra, if its monoid of endomorphisms has commuting idempotents. We show th…
An essential, hyperconnected, local geometric morphism that is not locally connected
Jens Hemelaer, Morgan Rogers
We give an example of an essential, hyperconnected, local geometric morphism that is not locally connected, arising from our work-in-progress on geometric morphisms $\mathbf{PSh}(M…
Monoid Properties as Invariants of Toposes of Monoid Actions
Jens Hemelaer, Morgan Rogers
We systematically investigate, for a monoid , how topos-theoretic properties of , including the properties of being atomic, strongly compact, local, totally con…
Duality for noncommutative frames
Karin Cvetko-Vah, Jens Hemelaer, Lieven Le Bruyn
We characterize the left-handed noncommutative frames that arise from sheaves on topological spaces. Further, we show that a general left-handed noncommutative frame arises fro…
Noncommutative Frames Revisited
Karin Cvetko-Vah, Jens Hemelaer, Jonathan Leech
In this note, we correct an error in arXiv:1702.04949 by adding an additional assumption of join completeness. We demonstrate with examples why this assumption is necessary, and di…
A topological groupoid representing the topos of presheaves on a monoid
Jens Hemelaer
Butz and Moerdijk famously showed that every (Grothendieck) topos with enough points is equivalent to the category of sheaves on some topological groupoid. We give an alternative,…
Grothendieck topologies on posets
Jens Hemelaer
Lindenhovius has studied Grothendieck topologies on posets and has given a complete classification in the case that the poset is Artinian. We extend his approach to more general po…
An arithmetic topos for integer matrices
Jens Hemelaer
We study the topos of sets equipped with an action of the monoid of regular matrices over the integers. In particular, we show that the topos-theoretic points are give…
Azumaya toposes
Jens Hemelaer
In arXiv:1606.07885, many different Grothendieck topologies were introduced on the category of Azumaya algebras. Here we give a classification in terms of sets of supernatural numb…
What is a noncommutative topos?
Karin Cvetko-Vah, Jens Hemelaer, Lieven Le Bruyn
In 1702.04949 noncommutative frames were introduced, generalizing the usual notion of frames of open sets of a topological space. In this paper we extend this notion to noncommutat…
Azumaya geometry and representation stacks
Jens Hemelaer, Lieven Le Bruyn
We develop Azumaya geometry, which is an extension of classical affine geometry to the world of Azumaya algebras, and package the information contained in all quotient stacks $[\ma…