As pointed out to me by Marta Bunge, the observation that the presheaf construction exhibits the free small-cocompletion for a small category is due to Pitts, and is proven as Corollary 1.3 of On product and change of base for toposes (1985). Andrew Pitts confirmed that he did not believe the result had been observed earlier, and was not part of the categorical folklore before that point.
varkor
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