and
nonabelian homological algebra
and
A graded object is often said to be of finite type if it is degreewise of finite dimension/rank, in some sense.
The terminology is used specifically in rational homotopy theory.
Notably a rational space is said to be of finite type if all its rational homotopy groups are finite dimensional vector spaces over the rational numbers.
Accordingly, chain complex of vector spaces, possibly that generating a semifree dga is said to be of finite type if it is degreewise finite dimensional.