categories: Re: categorical incunabula

[Andree Ehresmann <Andree.Ehresmann@u-picardie.fr>]

The list of MathSciNet publications that mention categories or functors
established by Peter Freyd is most interesting.

May I point to 2 important papers by Charles Ehresmann in this period
which, though not using the word "category", might also be relevant since
they extensively use "groupoids" (i.e., categories in which all the 
morphisms are invertible) and are at the root of a large part of the
subsequent work on categories done by and around Charles in the sixties? I
don't have access to the MathSciNet reference, but it should be easy to 
find.

1. Les prolongements d'une variete differentiable, Atti IV Congresso
 Unione Matematica Italiana, Taormina (1951), 1-9.
         In this paper Charles defines what will be later called "the 
category of infinitesimal jets" (between differentiable manifolds), with
its domain, codomain and composition maps, but without using the name
category (he said to me that he did not know of categories at this
date).
And he explicitly mentions that the invertible jets form a groupoid.

2. Les prolongements d'un espace fibre differentiable, C.R.A.S. Paris,
 240(1955 ), 1755-1757.
         Here Charles defines the action of a groupoid on a set and its
associated "principal groupoid" as a generalization of the fibre bundle
theory.  he had developed in the fourties. He also considers the
topological and differentiable cases, thus giving the first definition of
an "internal" groupoid and groupoid action. He applies this to study the
prolongations of manifolds.
His 1957 paper on categories (cited in the list) is a direct sequel of this
paper, except that the groupoids are then replaced by categories. And the
internal case has led in 1963 to his extensive study of  internal
categories and category actions (he used then the term "structured" instead
of "internal").

                         With my best wishes for all
                                 Andree C. Ehresmann