  We study 't Hooft anomaly matching in lattice models with strong Yukawa or
multi-fermion interactions. Strong non-gauge interactions among the mirror
fermions in a vectorlike lattice gauge theory are introduced with the aim to
obtain, in a strong-coupling symmetric phase, a long-distance unbroken gauge
theory with chiral fermions in a complex representation. We show how to use
exact lattice chirality to analyze the anomaly matching conditions on chiral
symmetry current correlators at finite lattice spacing and volume. We perform a
Monte Carlo study of the realization of anomaly matching in a toy
two-dimensional model with an anomalous mirror-fermion content at strong mirror
Yukawa coupling. We show that 't Hooft anomaly matching is satisfied, in most
of the phase diagram, via the minimal solution in either the massless fermion
or "Goldstone" mode, while in some cases there are extra massless vectorlike
mirror fermions. The mirror spectrum at strong coupling is thus consistent with
long-distance unitarity. We discuss the implications of our results for future
studies of the most interesting case of the decoupling of anomaly-free
mirror-fermion sectors.
