What is admittedly?

Some articles on admittedly:

Thirty Tyrants (Roman)
... never claimed Imperial dignity, 32 Titus admittedly not contemporary with Gallienus but Maximinus Thrax 33 Censorinus ... admittedly not contemporary with Gallienus but Claudius II Notwithstanding the author's pretensions regarding the time during which these persons aspired to the throne ...