Coalgebraic structures in module theory

Abstract

Abstract. Although coalgebras and coalgebraic structures are well-known for a long time it is only in recent years that they are getting new attention from people working in algebra and module theory. The purpose of this survey is to explain the basic notions of the coalgebraic world and to show their ubiquity in classical algebra. For this we recall the basic categorical notions and then apply them to linear algebra and module theory. It turns out that a number of results proven there were already contained in categorical papers from decades ago.