A characterization of long exact sequences coming from the snake lemma
Jan Stovicek
TL;DR
This paper characterizes the specific long exact sequences of length six that originate from the snake lemma within abelian categories, linking them to homology of triangles in derived categories.
Contribution
It provides a precise characterization of sequences arising from the snake lemma, connecting them to derived category homology.
Findings
Identifies conditions for sequences to come from the snake lemma
Connects long exact sequences to homology of triangles in derived categories
Clarifies the structure of sequences in abelian categories
Abstract
Given an abelian category, we characterize the long exact sequences of length six which can be obtained from the snake lemma. Equivalently, these are the long exact sequences which arise as the homology of a triangle in the corresponding derived bounded category.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Rings, Modules, and Algebras