Obstructions to compatible splittings
Representation Theory
2015-01-08 v1 K-Theory and Homology
Abstract
Suppose one has a map of split short exact sequences in a category of modules, or more generally, in any abelian category. Do the short exact sequences split compatibly, i.e., does there exist a splitting of each short exact sequence which commutes with the map of short exact sequences? The answer is sometimes yes and sometimes no. We define and prove basic properties of an obstruction group to the existence of compatible splittings.
Cite
@article{arxiv.1501.01389,
title = {Obstructions to compatible splittings},
author = {Andrew Salch},
journal= {arXiv preprint arXiv:1501.01389},
year = {2015}
}