# Algebra seminar

**Current seminar:**

## Septimiu Crivei (B.B.Univ. Cluj): Maximal Exact Structures on Additive Categories

**Abstract: **Quillen exact categories have recently reappeared into the mainstream due to some new applications to algebraic K-theory, model structures, approximation theory or functional analysis. They provide a suitable setting for developing homological algebra beyond abelian categories, as is often the case in the above settings. Every additive category has an obvious smallest exact structure given by the split exact sequences. It is natural to wonder whether there exists, and then which is, the greatest exact structure on an arbitrary additive category. We review known results for preabelian, weakly idempotent complete and additive categories, and we present some steps towards its description.

**Forthcomming:**

The Algebra Seminar was founded by Vladimir Korinek in the early 1950's and continued by Karel Drbohlav until 1981. The seminar resumed its activities in 1990 under the guidance of Jaroslav Jezek and Tomas Kepka. Since 1994, the seminar is headed by Jan Trlifaj.

Presently, the seminar is supported by GACR. It serves primarily as a platform for presentation of recent research of the visitors to the Department of Algebra as well as members of the Department and their students.