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  "body": "\n## Summary\n\nA Kan complex is a [[simplicial set|WW81ARB8K9]] in which every horn can be filled to a full simplex.\nKan complexes behave like topological spaces.\nTheir simplicial homotopy groups are well defined and agree with those of their geometric realization.\nThe singular simplicial set of every space is a Kan complex.\nKan complexes are the fibrant objects of the Kan–Quillen model structure on simplicial sets.\nThey are a standard model of $\\infty$-groupoids.\n\n## Explanations\n\n### L1 human\n\nA simplicial set is built from points, edges, triangles and higher simplices glued along faces.\nA horn is a simplex with one face and its interior removed, like two edges of a triangle that meet at a corner.\nIn a Kan complex every such horn is part of a full simplex, so two edges that meet can always be completed to a triangle.\nThis lets one compose and invert paths, as in a space.\nThe singular simplicial set of a space, whose $n$-simplices are all continuous maps from the standard $n$-simplex, is the basic example.\n",
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