In answer to John Baez Charles Ehresmann introduced internal categories to unify several examples of this notion that he had studied in earlier papers, namely topological and differentiable categories and specially groupoids (i.e. internal to Top and Diff) which he used extensively in his works on the foundations of differential geometry in the early fifties, ordered categories of several types (i.e. internal to sub-categories of the category of posets) also used in these works, and double categories (of which the 2-categories are a particular case) which he had introduced in his 1958 paper "Categorie des foncteurs types", Rev. Un. Mat. Argentina XX (1960). He defines the notion of internal categories (which he called "categorie structuree") and internal functors in the paper "Categories structurees", Ann. Ec. Normale Sup. 80 (1963), and internal natural transformations in the sequel of this paper "Categories structurees III: Quintettes et applications covariantes", Cahiers Top. et GD V (1963) where he constructs the double category of "quintettes structures" of which the 2-category of internal categories is a sub-2-category. However in these papers he defined only categories internal to a concrete category, which explains the name "categorie structuree". Later on he defined the general notion of an internal category, initially called "categorie structuree generalisee", in "Introduction to the theory of structured categories", Technical Report 10, Un. of Kansas at Lawrence, 1966 where he introduced the theory of sketches and, in particular, the sketch of a category. In this paper and in the paper "Categories structurees generalisees", Cahiers de Top. et GD X-1 (1968) he compares with the notion of a "C-category on (A,A0)" which Grothendieck had defined in 1960-61 by the fact that the Hom(A,-) are equipped with a natural strucutre of category. All the papers of Charles are reprinted in "Charles Ehresmann: Oeuvres completes et commentees", in the comments of which I give more historical information on this subject.. With all my best wishes for 2003 Andree C. Ehresmann