Apparaît dans la collection : Summer School 2026 - ICRA 2026

In this mini-course, we will introduce extriangulated categories, a notion that was developed as a common generalization of exact categories and triangulated categories. In Part I, Nakaoka will present the basic theory of extriangulated categories. Topics to be covered include the definition of extriangulated categories, exact and triangulated categories as typical examples, closure under extension-closed subcategories, ideal quotients by projective- injective objects, and a brief mention of 𝑛-exangulated categories. In Part II, Palu will mention some results that make use of extriangulated structures. First, the role of cotorsion pairs will be highlighted, mainly via Hovey’s correspondence. Then, the notion of a 0- Auslander extriangulated category will be introduced, and illustrated with several examples.