When is a category of adherence-determined convergences simple?

Abstract

Abstract. We provide a characterization of classes of filters $\mathbb{D}$ for which the full subcategory $\operatorname{fix}\operatorname{A}_{\mathbb D}$ of $\mathsf{Conv}$ formed by convergences determined by the adherence of filters of the class $\mathbb{D}$ is simple in $\mathsf{Conv}$. Along the way, we also elucidate when two classes of filters result in the same category of adherence-determined convergences. As an application of the main result, we show that the category of hypotopologies is not simple, thus answering a question from [25].