$L$-finite categories

Definition

A category $C$ is $L$-finite if the following equivalent conditions hold:

Remarks

The notion of L-finite category is a sort of categorification of the notion of K-finite set:

• A set $X$ is $K$-finite if the top element $1\in {\Omega }^{X}$ belongs to the closure of the singletons under finite unions.

• A category $C$ is $L$-finite if the terminal object $1\in {\mathrm{Set}}^{C}$ belongs to the closure of the representables under finite colimits.

References

• Robert Paré, Simply connected limits. Can. J. Math., Vol. XLH, No. 4, 1990, pp. 731-746, CMS

Revised on February 22, 2012 22:27:01 by Mike Shulman (71.136.234.110)