I have received answers to the six questions from Peter Johnstone and
Marta Bunge, and more generic responses from Michael Barr, Steve Awodey,
Ross Street and Francis Borceux. Martin Hyland and Ieke Moerdijk
explicitly refused to answer my questions. André Joyal organized a
private e-mail debate involving 9 persons to discuss the matter; the
people that took an active role in the debate were Joyal, myself, Peter
Johnstone and Laurent Lafforgue. Lafforgue deserves a special thanks for
his well-informed and extensive contribution to the discussion.
Following the debate, Joyal decided to issue a
public letter recognizing the originality of my “duality theorem”
and of the methodology ‘toposes as bridges’, to replace his initial
answer. The letter,
originally written in French,
concludes with the striking remark that the methodology ‘toposes as
bridges’ represents a vast generalization of Klein’s Erlangen program.
Responses
to the six questions by Peter Johnstone
Responses
to the six questions by Marta Bunge