  We set up a homological algebra for N-complexes, which are graded modules
together with a degree -1 endomorphism d satisfying d^N=0. We define Tor- and
Ext-groups for N-complexes and we compute them in terms of their classical
counterparts (N=2). As an application, we get an alternative definition of the
Hochschild homology of an associative algebra out of an N-complex whose
differential is based on a primitive N-th root of unity.
