Applied Categorical Structures – Official Blog

by Dzierzon, Christian

This paper presents a general construction, defining for each given strong generator $${\mathcal{G}}$$ in any locally finitely presentable category $$
{\mathbf{C}}
$$
an essentially algebraic, finitary theory $$
\Gamma _{{\mathbf{C}}}
$$
– maximal in a certain sense – such that $$
{\mathbf{C}}
$$ is equivalent to the category of models $$
{\mathbf{Mod}}{\left( {\Gamma _{{\mathbf{C}}} } \right)}
$$
of $$
\Gamma _{{\mathbf{C}}}
$$
. For regular generators $${\mathcal{G}}$$, generalization to the non-finitary case is easily done, and yields a new proof of the famous characterization of many-sorted quasivarieties.

DOI: 10.1007/s10485-005-9009-0
Online Date: 2/28/2006
Print publication date: 2/1/2006
View article on SpringerLink

by Simmons, Harold

I study the point-free and point-sensitive aspects of fitness, subfitness, and the difference between these two.

DOI: 10.1007/s10485-005-9010-7
Online Date: 2/18/2006
Print publication date: 2/1/2006
View article on SpringerLink

by Martínez, Jorge; Zenk, Eric R.

Nuclei which are defined over a class of frames are called nuclear typings. There is the dual notion of a spatial selector, and the relationship between nuclear typings and spatial selectors emanates from the duality between spatial frames and sober spaces. Especially interesting is the interplay between typings that are well-behaved with respect to certain frame quotients and selectors which similarly behave well in passage to closed sets.

DOI: 10.1007/s10485-005-9008-1
Online Date: 2/17/2006
Print publication date: 2/1/2006
View article on SpringerLink