6 papers · 1 filter
Normalizers in the category of topological groups
Maria Manuel Clementino, James Richard Andrew Gray
We show that the category of morphisms of topological groups admits split extension classifiers and hence the category of topological groups admits normalizers. We give explicit de…
A characterization of central extensions relative to n-nilpotent objects
Marino Gran, James R. A. Gray
We characterize the central extensions, in the sense of the categorical theory of central extensions of Janelidze and Kelly, relative to the Birkhoff subcategory of -nilpotent o…
More on action representability and normalizers
James Richard Andrew Gray
We show that under mild assumptions a functor is a prefibration if and only if it has terminal objects in its fibers and admits precartesian liftings of monomorphisms. We use this…
Observations on the variety of equationally linear Heyting semilattices
Xabier García-Martínez, James R. A. Gray, Michael A. Hoefnagel +2
In previous work, we analysed a number of categorical properties, of interest in the context of Janelidze-Márki-Tholen semi-abelian categories, for the variety of…
Categorical-algebraic aspects of Heyting semilattices
Xabier García-Martínez, James R. A. Gray, Michael A. Hoefnagel +2
This article gives an overview of some key categorical-algebraic properties of the variety of Heyting semilattices, with the aim of correcting a misconception in the literature. We…
Nice exact categories are coexact
James Richard Andrew Gray
Several important types of categories have been shown to be both exact and coexact (in the sense of Barr). The first type consists of abelian categories, which due to their self-du…