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Compatible structures in higher homological algebra

Amit Shah (Aarhus University)
Wednesday 8 December 2021 14:15–15:00 G3.1 (1532-314)
Mathematics Seminar

In joint work with R. Bennett-Tennenhaus, we called structure-preserving functors between extriangulated categories extriangulated functors. Examples include the canonical functor from an abelian category to its derived category, and the quotient functor from a Frobenius exact category to its stable category. The first, for example, is structure-preserving in the sense that short exact sequences are sent to distinguished triangles in a functorial way. In higher homological algebra, we also see examples of structure-preserving functors, but not covered by the current terminology. E.g. $n$-cluster tilting subcategories sitting inside an ambient abelian category. In ongoing work with R. Bennett-Tennenhaus, J. Haugland and M. H. Sandøy, we have been aiming to place these kinds of more general situations in a formal framework. This has led us to take a new perspective on extrianguated functors as I will explain.

Organised by: AarHomAlg
Contact: Peter Jørgensen Revised: 25.05.2023