# nLab projective limit

category theory

## Applications

#### Limits and colimits

limits and colimits

# Contents

## Idea

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.

Revised on July 21, 2014 06:42:04 by Urs Schreiber (89.15.239.100)