nLab projective limit



Category theory

Limits and colimits



Generally, a projective limit is the same thing as a limit. (Similarly, an inductive limit is the same thing as a colimit.) In this context, a projective system is the same thing as a diagram, and a projective cone is the same thing as a cone.

However, many authors restrict this terminology to limits over codirected sets (or cofiltered categories), especially the codirected set (,)(\mathbb{N},\geq) of natural numbers; see codirected limit (or cofiltered limit) for discussion of this case if you think that it may be what you want.

The dual concept is inductive limit.

Last revised on December 9, 2023 at 13:43:54. See the history of this page for a list of all contributions to it.