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  "body": "\n## Summary\n\nA subvariety of a [[variety|AJNZJD8442]] $\\mathcal{V}$ is a variety of the same signature that is contained in $\\mathcal{V}$.\nIt is obtained from $\\mathcal{V}$ by adding more identities.\nAbelian groups form a subvariety of groups, and distributive lattices form a subvariety of lattices.\nThe subvarieties of a variety form a lattice, which organises the classification of varieties.\n\n## Explanations\n\n### L1 human\n\nA variety is described by equations; a subvariety obeys those equations and some extra ones.\nAdding the equation $xy = yx$ to the group axioms gives the abelian groups.\nAdding $x^2 = e$ as well gives the abelian groups in which every element is its own inverse, the vector spaces over the field with two elements.\nEach extra equation can only shrink the class.\n",
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