In this 2013 paper, in Proposition 3.14, the author notes
$ \mathcal L(1) $ embeds in $ \mathbf L $, which embeds in $ \mathbf R $ the category of retracts of $ \mathcal L(1) $, so $ P \mathbf R \simeq P \mathbf L \simeq P \mathcal L(1) $ by Morita theory.
On nlab and wikipedia, I cannot find anything on Morita theory, other than for modules of rings. Is there a good resource on Morita theory for presheaves on categories? And what is the result (showing the equivalence of these three presheaf categories) that the author is referring to here?
Two categories have equivalent categories of presheaves iff their Cauchy completions (=idempotent completions) are equivalent. So if the categories are already Cauchy complete, this gives a stronger result.
A reference is Borceux and Dejean, Cauchy completion in category theory.