Can a cat be a co-author in academic paper? One of the most famous cat physicians must be F. D. Willard, who co-authored many physical papers.

My question is simple: 

Is it academically correct to have a cat/dog as a co-author of a paper, in principle? 
Does it correspond to the academic code of ethics? 
Does the author has to be a natural human?
Regarding whether or not all authors must be human, the answer seems to be no.

Combinatorist Doron Zeilberger, for example, has published many papers jointly with Salosh B. Ekhad (his name for his computer).