4 papers · 1 filter
Kaplansky classes and stability
Sean Cox
Soon after the proof of the Flat Cover Conjecture around the year 2000, two related concepts were introduced for classes in Grothendieck categories: \emph{Deconstructible classes}…
VopÄnka's Principle, Maximum Deconstructibility, and singly-generated torsion classes
Sean Cox
Deconstructibility is an often-used sufficient condition on a class of modules that allows one to carry out homological algebra \emph{relative to }. The…
Approximation properties of torsion classes
Sean Cox, Alejandro Poveda, Jan Trlifaj
We strengthen a result of Bagaria and Magidor~\cite{MR3152715} about the relationship between large cardinals and torsion classes of abelian groups, and prove that (1) the \emph{Ma…
Approximation Theory and Elementary Submodels
Sean Cox
\emph{Approximation Theory} uses nicely-behaved subcategories to understand entire categories, just as projective modules are used to approximate arbitrary modules in classical hom…