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  "body": "\n## Summary\n\nA cone over a [[diagram|HJK75HDWFE]] $D \\colon J \\to \\mathcal{C}$ is an object $N$, the apex, with a morphism from $N$ to each object $D(j)$ of the diagram.\nAll triangles formed with the morphisms of the diagram must commute.\nDually, a cocone has morphisms from the objects of the diagram into a common object.\nLimits are the universal cones and colimits are the universal cocones.\n\n## Explanations\n\n### L1 human\n\nPicture the diagram as a figure drawn on the floor and the apex $N$ as a point above it, with a string from $N$ down to each object.\nThe strings must be consistent with the arrows $D(j) \\to D(k)$ of the figure.\nGoing down to $D(j)$ and then along the arrow gives the same result as going down directly to $D(k)$.\nFor two sets $X$ and $Y$ with no arrows between them, a cone is just a set $N$ with two functions $N \\to X$ and $N \\to Y$.\n",
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