TITLE: Isomorphism in category of finite automata
QUESTION [7 upvotes]: What does meanthat two finite automata is equivalent? I think that we must define category of finite automata, i.e. we must define $\mathrm{Hom}(A,B)$, where $A,B$ be an arbitrary finite automata. Hence two finite automata $A,B$ are equivalent if there exist isomorphism $f\in\mathrm{Hom}(A,B)$. So, how we can define category of finite automata?

REPLY [2 votes]: The category of automata is discussed in Example 3.3. (3) in:
Adamek, Herrlich, Strecker - Abstract and concrete categories, the Joy of Cats, online.
It also appears in 4K, 5.2, 7.15, 13.13, 15.3, 20H in that book.