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  "body": "\n## Summary\n\nThe Auslander–Reiten quiver of a finite-dimensional algebra is a [[quiver|RE9YFFS3TS]] that maps out its module category.\nIts vertices are the isomorphism classes of [[indecomposable|E2P29GCD9T]] finitely generated modules, and its arrows record the irreducible morphisms between them.\nIt also carries the Auslander–Reiten translation $\\tau$, which makes it a translation quiver.\nFor algebras of finite representation type, it describes the whole module category.\nIts meshes come from the [[almost split sequences|M5D95FN7G3]].\n\n## Explanations\n\n### L1 human\n\nThe Auslander–Reiten quiver is a map of all the indecomposable modules of an algebra.\nEach module is a dot, and an arrow goes from one dot to another when there is a basic map between them that cannot be broken down further.\nThe almost split sequences show up as small diamond or triangle shapes, called meshes.\nFor the path algebra of $1 \\to 2$ the map has three dots, $S_2 \\to P_1 \\to S_1$.\nFor an algebra with infinitely many indecomposables, the quiver is infinite, but it still has a regular structure in many cases.\n",
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