# nLab direct limit

category theory

## Applications

#### Limits and colimits

limits and colimits

## (∞,1)-Categorical

### Model-categorical

The term direct limit is essentially another term for colimit, dating from a time before category theoretic terminology became established. It is still used in various areas of mathematics. (Dually, inverse limit is another term for limit.) In this terminology, direct system means diagram, and direct cone means cocone.

More specifically, the term direct limit is often understood by default to refer to colimits over directed sets (or filtered categories); see directed colimit (or filtered colimit) for discussion of this case.

Especially common here is the directed set $(\mathbb{N},\leq)$ of natural numbers, in which case the direct system may be called a direct sequence.

Last revised on April 24, 2021 at 03:36:56. See the history of this page for a list of all contributions to it.