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  "body": "\n## Summary\n\nUniversal algebra is the part of algebra that studies [[algebraic structures|QJGPT2W0FT]] in general, rather than groups, rings or lattices one at a time.\nIts objects are sets with a family of [[finitary operations|EJ8YJVM9BW]], described by a [[signature|WDVVEYD6AT]].\nIt treats [[homomorphisms|KBXSZC6BV1]], [[subalgebras|676H7EGTKJ]], [[congruences|DCSXXT4SER]] and products for all such structures at once.\nIts central results, such as [[Birkhoff's HSP theorem|5083DHSK82]], describe the classes of algebras defined by identities.\n\n## Explanations\n\n### L1 human\n\nGroups, rings, vector spaces and lattices are all sets with some operations that obey some rules.\nMany facts about them have the same proof: for example, the image of a homomorphism is always closed under the operations.\nUniversal algebra proves such facts once, for every kind of structure.\nFor example, a group is a set with a binary operation $\\cdot$, a unary operation ${}^{-1}$ and a constant $e$.\nA ring is a set with two binary operations, one unary operation and two constants.\nThe general theory then applies to both.\n",
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