For a positive integer $n$, the usual definitions of $n$-quasigroups are rather complicated: either by combinatorial conditions that effectively amount to Latin $n$-cubes, or by $2n$ identities on $n+1$ different $n$-ary operations. In this paper, a more symmetrical approach to the specification of $n$-quasigroups is considered. In particular, ternary quasigroups arise from actions of the modular group.

The class of all fibered automata is a variety of two-sorted algebras. This paper provides a full description of the lattice of varieties of fibred automata.