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](https://doi.org/10.1007/s002220100197), [pdf from the IAS](https://publications.ias.edu/sites/default/files/counterexample.pdf)