nLab inductive limit

Idea

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.

Related concepts

• ind-object, pro-object

• direct limit, another terminology for colimit