projective limit in nLab

Contents

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 (ℕ,≥)(\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.

• pro-object, ind-object

• inverse limit, another terminology for limit

• derived limit functor