nLab multilimit


A multilimit of a diagram F:DCF\colon D\to C in a category CC is a (small) set LL of cones over FF such that any cone over FF factors uniquely through a unique element of LL. Of course, limits are precisely multilimits for which LL is a singleton.

For example, the category Field of fields has no initial object, but it has a multi-initial-object, namely the family of all prime fields (in fact, this category is locally multipresentable).

Last revised on February 17, 2024 at 12:09:44. See the history of this page for a list of all contributions to it.