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  "body": "\n## Summary\n\nFor an endofunctor $F$ of a category, an $F$-coalgebra is an object $A$ with a morphism $A \\to F(A)$.\nIt is the dual of an $F$-algebra.\nCoalgebras model state-based systems such as automata, streams and transition systems.\nThe map describes what one can observe of a state and where it goes next.\nTerminal coalgebras give infinite data such as streams, and the uniqueness of maps into them gives proofs by coinduction.\n\n## Explanations\n\n### L1 human\n\nThink of $A$ as a set of states of a machine.\nThe coalgebra map tells, for each state, what the machine shows and what state comes next.\nFor example, with $F(X) = \\N \\times X$ on sets, take $A = \\N$ and send $n$ to $(n, n + 1)$.\nStarting at $0$, the machine shows $0, 1, 2, \\dots$ forever, which is an infinite stream.\n",
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