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


  1. There is a typo in (Pare) in the statement of this equivalence: it says “final” instead of “initial”.

Revised on May 22, 2014 13:41:33 by Mike Shulman (192.195.154.58)