# Cotorsion pairs and model structures (after Hovey ; Gillespie)

**Date**: Tuesday 23 May 2017, 14:00 – 15:00**Location**: Mathematics Level 8, MALL 1, School of Mathematics**Type**: Pure Mathematics seminars, Algebra seminars, Seminar series**Cost**: Free

#### Yann Palu, LAMFA, UPJV University of Amiens. Part of the algebra seminar series.

When k is a field and G a group, the module category Mod kG can be endowed with a model structure whose homotopy category is the stable category stmod kG. Hovey and Gillespie have generalised the constructions underlying this model structure to the case of (weakly idempotent complete) exact categories. In this generalisation, the role of the projective-injectives is played by two cotorsion pairs. Several applications to algebra (e.g. derived tensor product, recollements, generalisations of stable categories...) can thus be derived from homotopy theory via a relevant choice of cotorsion pairs. This talk will serve as an introduction to the results of Hovey and Gillespie. I might also talk about related results obtained with Hiroyuki Nakaoka.

*After each talk there will be tea/coffee in the Common Room at level 9 in Maths building. The current seminar organiser is Eleonore Faber. *

**Yann Palu**,* **LAMFA,UPJV University of Amiens *