nLab locally multipresentable category

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Contents

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 𝒞\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

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