nLab total derived functor

Idea

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.

Related concepts

• hyper-derived functor