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  "body": "\n## Summary\n\nA concrete category of algebras is a category whose objects are algebras of a fixed signature and whose morphisms are homomorphisms.\nIt comes with the [[forgetful functor|WV3BPYCHVG]] to sets.\nIt is the main example of a [[concrete category|FYBRP16KAN]]: objects are sets with structure, and morphisms are functions that respect the structure.\nVarieties, quasivarieties and other classes of algebras are studied in this setting.\nThere, notions such as monomorphism, epimorphism, free object and reflection can be compared with their set-based meanings.\n\n## Explanations\n\n### L1 human\n\nIn a concrete category every object has elements and every arrow is an honest function.\nGroups with group homomorphisms, rings with ring homomorphisms and lattices with lattice homomorphisms are all of this kind.\nBeing concrete makes some categorical notions easy to read: an injective homomorphism is a monomorphism, for instance.\nOther notions still surprise, since an epimorphism of rings need not be surjective.\n",
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