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  "body": "\n## Summary\n\nA prevariety is a class of algebras of one signature that is closed under isomorphic copies, [[subalgebras|7CHG6SD365]] and [[direct products|WJ73XYBNE4]].\nEvery [[quasivariety|WRXEKT4NQS]] and every [[variety|AJNZJD8442]] is a prevariety, but not conversely.\nThe prevariety generated by a class $K$ consists of the algebras that embed into a product of members of $K$.\nEvery prevariety is reflective: each algebra has a best approximation inside the class, as in the [[reflection onto a variety|6EWEMZ6FX1]].\n\n## Explanations\n\n### L1 human\n\nThink of a class of algebras that you can only enlarge by two moves: taking a part (a subalgebra) and putting several members side by side (a product).\nIf the class is stable under both moves, it is a prevariety.\nFor example, residually finite groups form a prevariety: a subgroup or a product of residually finite groups is again residually finite.\nFields do not, because the product of two fields has zero divisors.\n",
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