Pre-triangulated categories are triangulated
Category Theory
2015-06-17 v2 Algebraic Geometry
Algebraic Topology
K-Theory and Homology
Representation Theory
Abstract
We prove a stronger version of the octahedral axiom in a pre-triangulated category. The proof uses a new lemma about exact sequences in pointed additive categories which is based on a weak converse of the snake lemma.
Keywords
Cite
@article{arxiv.1506.00887,
title = {Pre-triangulated categories are triangulated},
author = {Antony Maciocia},
journal= {arXiv preprint arXiv:1506.00887},
year = {2015}
}
Comments
There is a serious error at the end of the proof of 3.4 which cannot be fixed. Thee is a counterexample to the statement of 3.4 due to Canonaco and Kunzer. Lemma 3.5 also needs stronger hypotheses. Many thanks to those whonsent comments, counterexamples and encouragement