Reference

Jan-Erik Roos made significant contributions to the study of derived functors of inverse limits, particularly in the context of homological algebra. One of his key contributions is the development of a systematic approach to understanding the derived functors of the inverse limit functor, often denoted as ( \varprojlim ). Roos explored the conditions under which these derived functors vanish, which has implications for the exactness of inverse limits in various categories.

His work helped clarify how these derived functors, especially the first derived functor ( \varprojlim^1 ), can be used to measure the failure of the inverse limit to be exact. This is particularly important in the study of modules, sheaves, and other algebraic structures where inverse limits are frequently used. Roos' insights have been instrumental in advancing the understanding of spectral sequences and their applications in algebraic topology and algebraic geometry.

Overall, Jan-Erik Roos' contributions provided a deeper understanding of the behavior of inverse limits in homological contexts, influencing subsequent research in the field.