Exact functor

Summary

An exact functor is an additive functor between abelian categories that sends short exact sequences to short exact sequences. Many natural functors, such as $\Hom(M, -)$ and $M \otimes -$, preserve only part of the exactness; they are called left exact or right exact. Measuring how far such a functor is from being exact is the purpose of derived functors such as Ext and Tor.