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  "body": "\n## Summary\n\nA simplicial object in a [[category|A2DE66937D]] $\\mathcal{C}$ is a contravariant [[functor|28NQ0KRHD3]] from the [[simplex category|FRFYHJGAN3]] to $\\mathcal{C}$.\nIt is a sequence of objects $X_0, X_1, X_2, \\dots$ of $\\mathcal{C}$ with face and degeneracy maps between them that obey the simplicial identities.\nIn $\\mathcal{C} = \\mathbf{Set}$ these are the [[simplicial sets|WW81ARB8K9]], and in abelian groups they are the simplicial abelian groups of the [[Dold–Kan correspondence|PY4EWJ8BQA]].\nThey let one do homotopy theory with objects of $\\mathcal{C}$.\n\n## Explanations\n\n### L1 human\n\nThink of $X_n$ as the \"$n$-dimensional pieces\" of a shape built from points, edges, triangles and higher simplices.\nThe face maps send a piece to its faces, and the degeneracy maps view a piece as a flattened piece one dimension up.\nIn a simplicial object, each $X_n$ is not a mere set but an object of some category, such as a group or a space.\nFor example, the constant simplicial object on an object $A$ has $X_n = A$ for all $n$ and all face and degeneracy maps equal to the identity.\n",
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