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  "body": "\n## Summary\n\nTame congruence theory is a structure theory for finite algebras and [[locally finite varieties|8QPW65PZVW]], developed by David Hobby and Ralph McKenzie.\nIt studies each covering pair $\\alpha \\prec \\beta$ in the [[congruence lattice|REE07CSXHR]] of a finite algebra through the polynomial operations restricted to small subsets, the minimal sets.\nOn these subsets the algebra behaves in one of five ways, which gives each covering pair a type: unary, affine, Boolean, lattice or semilattice.\nThe types that occur in a locally finite variety control its congruence lattices and its Mal'cev conditions.\nFor example, a locally finite variety omits the unary type exactly when it has a [[Taylor term|QEAMRNRJJD]].\n\n## Explanations\n\n### L1 human\n\nA finite algebra can be very complicated, but tame congruence theory looks at it one small step at a time.\nEach step goes from one congruence to the next larger one, and the theory finds a small piece of the algebra where this step is visible.\nOn that piece, the algebra looks like one of five simple kinds of structure: a set with permutations, a vector space, a Boolean algebra, a lattice, or a semilattice.\nKnowing which kinds appear tells a great deal about the whole algebra and the variety it generates.\n",
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