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  "body": "\n## Summary\n\nThe Ind-completion $\\mathrm{Ind}(\\mathcal{C})$ of a category $\\mathcal{C}$ is the category of formal [[filtered|975PMY4FG8]] colimits of objects of $\\mathcal{C}$.\nIts objects are called ind-objects.\nIt is the free way to add filtered colimits to $\\mathcal{C}$, and it can be realized inside the category of [[presheaves|AND2WHZC8P]] on $\\mathcal{C}$.\nFor example, the Ind-completion of finite sets is the category of all sets.\n\n## Explanations\n\n### L1 human\n\nSome objects are best seen as limits of growing chains of simpler objects.\nAn infinite set is the union of its finite subsets, and an infinite-dimensional vector space is the union of its finite-dimensional subspaces.\nThe Ind-completion adds such unions formally, even when the original category does not contain them.\nSo starting from finite-dimensional vector spaces, the Ind-completion gives all vector spaces.\n",
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