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