Algebraic model categories and applications

Constanze Roizheim (Glasgow)

Wednesday 22nd October, 2008 16:00-17:00 214

Abstract

Model categories are a method to define a homotopy relation between morphisms in a category. They first arose in a topological context, but also lots of "algebraic" categories fit into this framework, e.g. chain complexes of modules over a ring. So, roughly speaking, one can model homotopy-theoretic constructions in the algebraic world. By generalised Morita theory a lot of information about a model categories is captured in certain endomorphism objects. For algebraic model categories, the relevant endomorphism objects are differential graded algebras. Hence, studying the homotopical properties of algebraic model categories leads to moduli problems in homological algebra. We are going to explain this concept and present some examples of classification problems.

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