A **multilimit** of a diagram $F\colon D\to C$ in a category $C$ is a (small) set $L$ of cones over $F$ such that any cone over $F$ factors uniquely through a unique element of $L$. Of course, limits are precisely multilimits for which $L$ is a singleton.

For example, the category Field of fields has no initial object, but it has a multi-initial-object, namely the family of all prime fields (in fact, this category is locally multipresentable).

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