I report below Steve Awodey's response to my request of clarification (in italic), followed by my commentary to it.
Dear Olivia,
I assume you are
responding to some negative experiences you have had, and I’m sorry
about that.
I hope you will
get some valuable replies to your survey, but I myself prefer not to
answer the questions in detail.
One thing I can say is that I have also felt that the field of topos
theory is not a good area for new researchers, in part because some of
the experts know a lot more than they have published.
Also, there are some people in the field who will easily
know almost anything that you can come up with, even if they have not
thought of it before, and so you will not get the credit or due respect
for even previously unpublished results.
My own response
to this problem was to look for other areas than topos theory to work
in, preferably ones in which those experts were not also working.
Intensional
Martin-Löf type theory seemed pretty safe, but that hasn’t exactly
worked out as I expected.
I would advise
you to also look for new areas where you will not have to compete with
the accumulated wisdom of the last 40 years, and the people who hold it.
It’s not good
for topos theory, but maybe topos theory needs a little break.
Best wishes for
a happy new year,
Steve
This letter
confirms the
attitude of
some
experts in topos theory from the old generation to dismiss the work of
young researchers on the subject on the grounds that they knew
everything already, even though they have not cared to write it down.
Moreover,
it shows an aprioristic attitude from Awodey himself
towards the results that I *could* obtain in my research, as opposed to
the results that I have already obtained: how can one say that
"almost
anything
that you can come up with" will be
"easily known"
by some experts? I did not suspect that some experts
in topos theory had also the ability to read in the future!
Of course, this kind
of intimidation and abuse of power from people from the old generation
who hold academic posts with regard to young researchers in a precarious
position should not be tolerated by someone who is already in the
‘system’, such as Steve Awodey. Quite astonishingly, not only this is
accepted, but he even
suggests me to
change field of research! The theory of classifying toposes has already
remained essentially dormant for forty years: this is no “little break”,
and there is no rational reason why this rich and beautiful subject
should remain undeveloped any longer.
To better understand Awodey’s reaction to my request for clarification, it is appropriate to recall that he has explicitly dismissed my work in a Mathscinet review of one of my papers as "straightforward considerations involving classifying toposes" (see here for more details). He also wrote another erroneous MathSciNet review of a paper of mine, namely "A general method for building reflections". This review clearly shows that Awodey has not properly understood the paper. He writes that
The description of an adjunction between two categories as an equivalence of certain comma categories, given in F. W. Lawvere's 1963 thesis is applied to geometric morphisms between toposes to generate Stone-type dualities of the kind previously studied in the author's paper "A topos-theoretic approach to Stone-type dualities".
There are two mistakes in this paragraph:
(1) It is not true that Lawvere's description of an adjunction in terms of certain comma categories is *applied* in my paper to generate dualities or reflections. Lawvere's work was cited in the introduction of my paper just to provide a philosophical underpinning for the approach undertaken in the paper, in addition to that provided by the 'toposes as bridges' philosophy which is also cited in that context, but the general technical framework developed in the paper, as well as its corollaries, are *not* applications of Lawvere's result.
(2) As the title of my paper indicates, the focus is *not* on generating dualities, but reflections. In particular, no new *dualities* are introducted with respect to my preprint "A topos-theoretic approach to Stone-type dualities"; rather, by applying the general framework developed in the first part of the paper, *reflections* which extend the dualities obtained in that preprint are obtained.
Once again, Awodey's mistakes have the unfortunate
effect