  We extend the functorial approach to automata by Colcombet and Petri\c{s}an
[arXiv:1712.07121] from the category of sets to any elementary topos with a
natural number object and establish general Myhill-Nerode theorems in our
setting. As a special case we recover the result of Boja\'nczyk, Klin and
Lasota [arXiv:1402.0897] for orbit-finite nominal automata by considering
automata in the Myhill-Schanuel topos of nominal sets.
