nLab m-finite spaces

Definition

Definition

A connected space $X$ is $m$-finite for $m \in \mathbb{N}$ if

• $X$ is m-truncated, and

• $\pi_k(X)$ is finite, and for all $k$.

A space is $m$-finite if it’s a finite disjoint union of $m$-finite connected spaces; a space is $\pi$-finite if it’s $m$-finite for some $m \in \mathbb{N}$.

Related concepts

• semiadditive (∞,1)-category

• m-commutative monoid

References

• Michael Hopkins, Jacob Lurie, Ambidexterity in K(n)-Local Stable Homotopy Theory (2014)