  In the context of two-player games over graphs, a language $L$ is called
positional if, in all games using $L$ as winning objective, the protagonist can
play optimally using positional strategies, that is, strategies that do not
depend on the history of the play. In this work, we describe the class of
parity automata recognising positional languages, providing a complete
characterisation of positionality for $\omega$-regular languages. As
corollaries, we establish decidability of positionality in polynomial time,
finite-to-infinite and 1-to-2-players lifts, and show the closure under union
of prefix-independent positional objectives, answering a conjecture by
Kopczy\'nski in the $\omega$-regular case.
