Degenerating $0$ in Triangulated Categories
Representation Theory
2019-01-29 v1 Category Theory
Rings and Algebras
Abstract
In previous work, based on work of Zwara and Yoshino, we defined and studied degenerations of objects in triangulated categories analogous to degeneration of modules. In triangulated categories it is surprising that the zero object may degenerate. We study this systematically. In particular we show that the degeneration of the zero object actually induces all other degenerations by homotopy pullback, that degeneration of is closely linked, but not equivalent, to having zero image in the Grothendieck group.
Keywords
Cite
@article{arxiv.1901.09713,
title = {Degenerating $0$ in Triangulated Categories},
author = {Manuel Saorín and Alexander Zimmermann},
journal= {arXiv preprint arXiv:1901.09713},
year = {2019}
}