# nLab inductive limit

category theory

## Applications

#### Limits and colimits

limits and colimits

# Contents

## 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.

Revised on July 21, 2014 06:40:11 by Urs Schreiber (89.15.239.100)