nLab inductive limit



Category theory

Limits and colimits



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

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

The dual concept is that of a projective limit.

Last revised on December 9, 2023 at 13:43:38. See the history of this page for a list of all contributions to it.