Notes on Triangulated Categories
Tobias Fritz
TL;DR
This paper provides an accessible introduction to triangulated categories, focusing on their axioms, homological algebra, subcategories, and localization, with minimal axioms and illustrative examples.
Contribution
It offers a simplified, axiomatic approach to triangulated categories, emphasizing minimal assumptions and derivations, along with comprehensive examples.
Findings
Derived all statements from minimal axioms
Established existence of biproducts from axioms
Presented diverse examples of triangulated categories
Abstract
We give an elementary introduction to the theory of triangulated categories covering their axioms, homological algebra in triangulated categories, triangulated subcategories, and Verdier localization. We try to use a minimal set of axioms for triangulated categories and derive all other statements from these, including the existence of biproducts. We conclude with a list of examples.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra