Ind-completion

Summary

The Ind-completion $\mathrm{Ind}(\mathcal{C})$ of a category $\mathcal{C}$ is the category of formal filtered colimits of objects of $\mathcal{C}$. Its objects are called ind-objects. It is the free way to add filtered colimits to $\mathcal{C}$, and it can be realized inside the category of presheaves on $\mathcal{C}$. For example, the Ind-completion of finite sets is the category of all sets.