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Homological algebra as a stable homotopy theory

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If you have a question about this talk, please contact Zhen Lin Low.

There is a well-known analogy between the homological algebra of chain complexes of abelian groups and the stable homotopy theory of spectra. I will try to explain how homological algebra in an abelian category is an example of an abstract stable homotopy theory, using the formalism of categories of fibrant objects. Time permitting, I may also explain how to think about the dreaded octahedral axiom of triangulated categories from the perspective of homotopy theory.

No knowledge of homotopy theory (either classical, stable, or abstract) will be assumed in this talk.

This talk is part of the Extraordinary Category Theory Seminar series.

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