nLab
finite type

Context

Homological algebra

homological algebra

and

nonabelian homological algebra

Context

Basic definitions

Stable homotopy theory notions

Constructions

Lemmas

diagram chasing

Homology theories

Theorems

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 (82.113.99.28)