We show that the sets of d-dimensional Latin hypercubes over a non-empty set X, with d running over the positive integers, determine an operad which is isomorphic to a sub-operad of the endomorphism operad of X. We generalise this to categories with finite products, and then further to internal versions for certain Cartesian closed monoidal categories with pullbacks.
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Markus Linckelmann (2024) studied this question.
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