finite type


Homological algebra

homological algebra


nonabelian homological algebra


Basic definitions

Stable homotopy theory notions



diagram chasing

Homology theories


Rational homotopy theory

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.

Beware however that the terminology clashes with the use in homotopy theory, there the concept of finite homotopy type is crucially different from homotopy type with finite homotopy groups.

Revised on February 2, 2014 07:11:49 by Urs Schreiber (