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 noncommutative Grothendieck… Expand

Abstract We study the topos of sets equipped with an action of the monoid of regular 2 × 2 matrices over the integers. In particular, we show that the topos-theoretic points are given by the double… Expand

We extend Grothendieck topologies on commutative algebras to the category of all Azumaya algebnas and we show that the functor assigning to an Azumaaya algebra $A$ the set of all algebra maps $R \to A$ from a fixed $\mathbb{C}$-algebra $R$, is a sheaf.Expand

In [4], many different Grothendieck topologies were introduced on the category of Azumaya algebras. Here we give a classification in terms of sets of supernatural numbers. Then we discuss the… Expand

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 posets, by… Expand

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 $[\mathrm{rep}_n… Expand

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 $\mathbf{PSh}(M) <- PSh(N)$, where $M$ and $N$ are monoids.Expand