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  "body": "\n## Summary\n\nA direct limit, or inductive limit, is the [[colimit|BJS1CGTKQ5]] of a system of objects indexed by a [[directed set|D9RY4667K6]].\nIts maps go from earlier objects to later ones.\nIt builds a large object as the union of a growing family of smaller ones.\nMany objects of algebra are built this way, such as the [[Prüfer group|F0XAMM2PPS]] and stalks of sheaves.\nThe dual notion is the [[inverse limit|DZB378CNCK]].\n\n## Explanations\n\n### L1 human\n\nPicture a chain of boxes, each one placed inside the next.\nThe direct limit is the big box that holds all of them at once.\nTwo elements of the boxes count as the same once they become equal in some later box.\nFor example, the groups $\\frac{1}{2^n}\\Z$ for $n = 0, 1, 2, \\dots$ sit inside each other.\nTheir direct limit is the group of all fractions whose denominator is a power of $2$.\n",
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