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  "body": "\n## Summary\n\nThe fundamental groupoid $\\Pi_1(X)$ of a topological space $X$ is a groupoid.\nIts objects are the points of $X$, and its morphisms are paths up to [[path homotopy|CCNKA8C711]].\nIt records the [[fundamental group|S1XK3HXHFX]] at every base point at once, together with the paths that compare them.\nIt needs no choice of base point, which makes some results, such as versions of the Seifert–van Kampen theorem, easier to state and prove.\n\n## Explanations\n\n### L1 human\n\nThe fundamental group looks only at loops from one chosen point.\nThe fundamental groupoid looks at all paths between all pairs of points, up to deformation with fixed ends.\nPaths can be composed when the end of one is the start of the next, and every path can be run backwards.\nFor a space made of two separate pieces, the groupoid sees both pieces, while a fundamental group sees only the piece of its base point.\n",
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