total derived functor

(also nonabelian homological algebra)

In the context of derived functors in homological algebra one often says “$k$th derived functor” for the $k$th chain homology of a functor applied to a suitable resolution. Omitting the passage to homology here is then called forming the *total derived functor*. In more general contexts of homotopy theory, that total derived functor would simply be called the *derived functor* itself.

See at *derived functor in homological algebra* for a detailed discussion.

Revised on September 16, 2017 14:21:55
by Zoran Škoda
(212.91.105.243)