Abstract
A famous theorem by Baker and Pixley states that the term functions of a finite algebra with a (d + 1)-ary near-unanimity term are precisely the functions under which all subalgebras of the algebra's dth power are closed. In this paper, we generalize the theorem to a completely abstract level. Indeed, we obtain a version of the theorem that is stated in purely category-theoretic terms, making it applicable in any concrete or abstract category. To motivate this rather abstract result, we also discuss some of its concrete applications.
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