A characterisation of n-exangulated functors

Abstract: Examples of structure-preserving functors between extriangulated categories, so-called extriangulated functors, 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 an attempt, with R. Bennett-Tennenhaus, J. Haugland and M. H. Sandøy, to place these kinds of more general situations in a formal framework, we have been led to a new perspective on extriangulated (or, more generally, n-exangulated) functors. The aim of my talk is to explain this.

combinatoricscategory theoryrepresentation theory

Audience: researchers in the topic

The TRAC Seminar - Théorie de Représentations et ses Applications et Connections