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In computability and complexity, finding mappings between problems that allow solving one problem using a solution of another one. For reduction in programming language theory (e.g. beta-reduction), see [lambda-calculus] or [term-rewriting].
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"Functorial" reductions?
Another analogy may be made with linear algebra: functorial reductions would be linear maps wheras $\mathsf{NC}^0$ reductions are affine maps). … I am pretty sure that "functorial" reductions are too restrictive to be of general interest. For instance, I do not see how CIRCUIT VALUE could be $\mathsf P$-complete under such reductions. …