# nLab projective limit

category theory

## Applications

#### Limits and colimits

limits and colimits

## (∞,1)-Categorical

### Model-categorical

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.

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.

Revised on July 28, 2011 02:04:22 by Toby Bartels (76.85.192.183)