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  "body": "\n## Summary\n\nThe solution set condition on a [[functor|28NQ0KRHD3]] $G \\colon \\mathcal{D} \\to \\mathcal{C}$ asks the following.\nFor each object $c$, a mere set of morphisms $c \\to G d$ is enough to factor all of them.\nIt is a smallness condition.\nTogether with completeness and preservation of limits, it gives the existence of a left [[adjoint|TZHF6ZM92S]] in Freyd's adjoint functor theorem.\n\n## Explanations\n\n### L1 human\n\nTo build a free group on a set $X$, one would like to look at all maps from $X$ into all groups at once.\nThere are too many groups for that to be a set.\nBut every such map lands in the subgroup generated by its image, and that subgroup is not much bigger than $X$.\nSo a set of small groups is enough to see all maps from $X$.\nThe solution set condition asks for such a set in general.\n",
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