It was "proved" in 1961 that the first right derived functor, $\lim^1_{\leftarrow}$ of the inverse limit functor is zero on Mittag-Leffler systems.
However, recently a counter-example was found by Neeman and Deligne:
- Neeman, A. A counterexample to a 1961 “theorem” in homological algebra, Invent. math. 148, 397–420 (2002). doi:10.1007/s002220100197, pdf from the IAS
