categories: Cartesian closed categories of internal categories

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

In answer to Philippe Gaucher who asks for

 >a bibliographical reference for the following theorem : "consider a
 complete
 >cocomplete cartesian closed category C. Then the category of internal 1-
 >categories of C is complete cocomplete and cartesian closed".

This theorem (and also a more general one for models of a sketch in a
category ) has been proved in our paper:

         "Categories of sketched structures",
         by Andree Bastiani (my maiden name) and Charles Ehresmann,
         Cahiers de Top. et Geom. Diff. XIII-2 (1972), 1-107,  reprinted in
         "Charles Ehresmann; Oeuvres completes et commentees" Part IV-2,
         pp. 407-517.

In particular, in Sections 12 and 13 we give two constructions, one valid
for all sketches, the other particular to the case of internal categories.
This last construction generalizes a construction we had given in a
preceding paper:
         "Categories de foncteurs structures", Cahiers TGD XI-3 (1969),
329-384,         reprinted in the Oeuvres Part IV-1
in the case of categories internal to a concrete category.

         Hoping these old references may be of some help,
                 Sincerely

Professeur Andree C. Ehresmann
Faculte de Mathematique et Informatique
33 rue Saint-Leu
F-80039 Amiens. France

Directeur des "Cahiers de Topologie
et Geometrie Differentielle categoriques"

e-mail:   ehres@u-picardie.fr

Site Internet:   http://perso.wanadoo.fr/vbm-ehr