URegina Topology Seminar: Sebastian Martensen

Triangulated categories were introduced to capture some of the extra structure present in the derived category of a ring and the stable homotopy category, and today they are present wherever homological algebra plays a central role. In the case of derived categories, the triangulation captures certain “shadows” of short and long exact sequences, and so one may wonder: are there categories that capture only long exact sequences of a certain length? This led to the introduction of n-angulated categories in 2013 by Geiss, Keller, and Oppermann. Today, they find their use in representation theory, and it is a hope that they will one day play a role in topology as well. For this talk we will discuss triangulated categories, stable module categories, and introduce n-angulated categories along with their main class of examples.