Olivia Caramello's website

 

Unifying theory

Controversy with category theorists

Responses to the initiative of clarification

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.

I would like to stress that, contrary to the persistent accusation of proving "well-known" results which I have been receving throughout the past years, none of the contacted experts was able to provide a single reference containing a proof or a statement of a result that I attributed to myself but which had been proved before, nor anyone showed that any of my results could be deduced from previously existing results in an essentially straightforward way.

Letter by André Joyal

Responses to the six questions by Peter Johnstone

Responses to the six questions by Marta Bunge

Reply by Francis Borceux

Reply by Ross Street

Reply by Steve Awodey

Reply by Michael Barr