We will first introduce model categories, which are structures which axiomatize some of the typical tools one uses in classical homotopy theory. Second, we will show that the structure of a model category exists also in algebraic contexts, such as on categories of chain complexes, and via these structures we will see a close link to homological algebra. Third, we will discuss homotopy limits and colimits and, more generally, how model structures allow us to construct derived categories and derived functors, including the construction of the classical derived category of an abelian category.

Speaker(s): Montek Gill (UM)