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  "body": "\n## Summary\n\nAn accessible category is a large category that is generated, under highly [[filtered colimits|975PMY4FG8]], by a small set of small objects.\nHere small objects are the $\\lambda$-presentable ones, those whose hom functor preserves $\\lambda$-filtered colimits for a [[regular cardinal|13ZV2F8JAR]] $\\lambda$.\nAccessible categories are exactly the categories of models of sketches, and they include the categories of models of many first-order theories.\nThe cocomplete ones are the locally presentable categories.\n\n## Explanations\n\n### L1 human\n\nMany large categories are determined by a small part of them.\nEvery set is the union of its finite subsets, and every vector space is the union of its finite-dimensional subspaces.\nAn accessible category is one where every object is glued in this way from a fixed small stock of small objects.\nThis lets one handle a huge category with set-sized data.\n",
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