a note on sources of my text of fibered categories

[Thomas Streicher <streicher@mathematik.tu-darmstadt.de>]

> Renewed study of these ideas, in light of the later exposition by
> Thomas Streicher, should lead to further applications (for example
> to the solution of problems posed in my 1972 Perugia Notes.)

Thanks for mentioning this text. But since I think ownership of ideas
is an important issue I want to point out that the aim of this text
was to exhibit part of the ideas and results of Jean B'enabou's almost
single handed approach to Fibered Categories as a foundation of
Category Theory over most general base categories. I also tried to explain
some work by J.-L. Moens (his 1982 Thesis) where I think I have added
a bit of additional material. As far as B'enabou's work is concerned
my sources were Roisins notes from B'enabou's 1980 Louvain-la-Neuve
lectures. My exposition evolved over the years and I have integrated
additional material and made corrections as I learnt from Jean for
which I am very grateful to him.

At one place I have referred to a fibred version of the Special
Adjoint Functor Theorem which one can find in Par'e and Schumacher's
text or alternatively in J.Celeyrette's These d'Etat from 1974 under
supervision of B'enabou.

The references in my text are not exhaustive at all. It's certainly a
mistake not to have formally referred to work by Grothendieck and Giraud.
But I was not using too much these original sources.

Moreover, I have used results from a paper by Mamuka Jibladze. I have
not given the precise reference but made clear in the title of the
appendix that it is Mamuka's result.

The aim of these notes was not to document precisely who did
what. However, on the first page I clearly stated whose work
influenced me!

I am also aware that in Bill's "Perugia Notes" one can find the idea
that fibered or indexed categories are suitable for doing category
theory over a base topos. But as I said it wasn't my intention to
document the history of ideas but rather to write up the view of
things as I learnt it from Jean's work and private communications.

Thomas Streicher



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