nLab
L-finite category

LL-finite categories

Definition

A category CC is LL-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 XX is KK-finite if the top element 1Ω X1 \in \Omega^X belongs to the closure of the singletons under finite unions.

  • A category CC is LL-finite if the terminal object 1Set C1\in 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)