We give an explicit correspondence between stated skein algebras, which are defined via relations on tangles in [Costantino F., L\^e T.T.Q., arXiv:1907.11400], and internal as endomorphism algebras free cocompletions of categories [Ben-Zvi D., Brochier A., Jordan J. Topol. 11 (2018), 874-917, arXiv:1501.04652] or [Gunningham S., Safronov P., arXiv:1908.05233]. Stated surfaces with multiple boun...