nLab locally multipresentable category

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.

Related concepts

• locally presentable category

• locally polypresentable category

• multicolimit

References

The definition is due to

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