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Hello all. I have a pre-cosheaf in the category of vector spaces. How do I cosheafify? I've failed to find literature on this topic.

I'll be more specific. Let $\mathbb{X}$ be a topological space and $\mathbf{Open}(\mathbb{X})$ the open set category of $\mathbb{X}$. Let $\mathbf{Vect}$ be the category consisting of real vector spaces as its objects and linear maps as its morphisms. My pre-cosheaf is a functor $\mathsf{F} : \mathbf{Open}(\mathbb{X}) \to \mathbf{Vect}$. How do I cosheafify $\mathsf{F}$?

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# Cosheafification

Hello all. I have a pre-cosheaf in the category of vector spaces. How do I cosheafify? I've failed to find literature on this topic.