Rectangular torsion theories

Published in Preprint, 2025

Joint work with Elena Caviglia and Zurab Janelidze.

In this paper we introduce and study rectangular torsion theories, i.e. those torsion theories (C,T,F) with C a pointed category, where the canonical functor C->TxF is an equivalence of categories. In particular, we show that these are precisely the internal rectangular bands in the 2-category of pointed categories.