  We revisit the question of whether a two-dimensional topological insulator
may arise in a commensurate N\'eel antiferromagnet, where staggered
magnetization breaks both the elementary translation and time reversal, but
retains their product as a symmetry. In contrast to the so-called $Z_2$
topological insulators, an exhaustive characterization of antiferromagnetic
topological phases with the help of a topological invariant has been missing.
We analyze a simple model of an antiferromagnetic topological insulator and
chart its phase diagram based on a recently proposed criterion for
centrosymmetric systems [Fang et al., Phys. Rev. B 88, 085406 (2013)]. We then
adapt two methods, originally designed for paramagnetic systems, and make
antiferromagnetic topological phases manifest. The proposed methods apply far
beyond the particular example treated in this work, and admit straightforward
generalization. We illustrate this by considering a non-centrosymmetric system,
where there are no simple criteria to identify topological phases. We also
present an explicit construction of edge states in an antiferromagnetic
topological insulator.
