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  "body": "\n## Summary\n\nA complete atomic Boolean algebra is a [[complete Boolean algebra|75BPV95AAS]] in which every nonzero element lies above an [[atom|TTVCTW6TNC]].\nEvery power set algebra is of this kind.\nConversely, every complete atomic Boolean algebra is isomorphic to the power set of its set of atoms.\nSo these algebras are the same as sets, seen algebraically.\nWith homomorphisms that preserve all suprema, their category is dual to the category of sets.\n\n## Explanations\n\n### L1 human\n\nAn atom is a smallest nonzero element, like a single point among the subsets of a set.\nIn a complete atomic Boolean algebra, every element is built from the atoms below it, and every collection of atoms builds an element.\nSo the algebra is just the family of all subsets of its atoms.\nFor example, the subsets of $\\set{1, 2, 3}$ form such an algebra with the three atoms $\\set{1}$, $\\set{2}$, $\\set{3}$.\n",
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