  Using the categorical approach to Poincar\'e-Birkhoff-Witt type theorems from
our previous work with Tamaroff, we prove three such theorems: for universal
enveloping Rota-Baxter algebras of tridendriform algebras, for universal
enveloping Rota--Baxter Lie algebras of post-Lie algebras, and for universal
enveloping tridendriform algebras of post-Lie algebras. Similar results, though
without functoriality of the PBW isomorphisms, were recently obtained by
Gubarev. Our methods are completely different and mainly rely on methods of
rewriting theory for shuffle operads.
