Pre-triangulated categories are triangulated
Antony Maciocia
TL;DR
This paper strengthens the octahedral axiom in pre-triangulated categories using a novel lemma about exact sequences, advancing the theoretical understanding of these structures.
Contribution
It introduces a new lemma based on a weak converse of the snake lemma to prove a stronger version of the octahedral axiom.
Findings
Established a stronger octahedral axiom in pre-triangulated categories
Developed a new lemma related to exact sequences in additive categories
Enhanced theoretical foundations of triangulated category 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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra