# nLab locally multipresentable category

Contents

category theory

## Applications

#### Compact objects

objects $d \in C$ such that $C(d,-)$ commutes with certain colimits

# Contents

## Idea

A locally multipresentable category is similar to a locally presentable category, but where we ask only for the existence of connected limits rather than all small limits.

## Definition

###### Definition

(locally multipresentable category)

A category $\mathcal{C}$ is called locally multipresentable if

1. it is an accessible category;

2. it has all connected limits.

The second condition is equivalent to:

2’. it has all small multicolimits.

## References

The definition is due to

• Yves Diers. Catégories localisables. Diss. Paris 6 et Centre universitaire de Valenciennes et du Hainaut Cambrésis (1977)

Created on July 29, 2022 at 12:14:17. See the history of this page for a list of all contributions to it.