Let me advertise for some more or less recent work of mine about sketches/accessible categories (not available electronically, but I'll be happy to send reprints or preprints on request). ------- (1) Cat'egories accessibles `a limites projectives non vides et cat'egories accessibles `a limites projectives finies Diagrammes 34 (1995) 1-10 For fixed b, b-accessible categories with non-empty limits are characterized as the categories of models of specific sketches. As a corollary, the category of these categories is Cartesian closed. (Proved independantly by Ad'amek.) Accessible categories with finite limits are also characterized. ------- (2) Effective taxonomies and crossed taxonomies Cahiers de Top. et de G'eom. Diff. Cat. XXXVII (1996) 82-90 A taxonomy is a "category without identities". This bare structure is somewhat dull, but "crossed modules of taxonomies" seem more interesting. In the latter structure, "Dedekind-finite" objects play a role similar to that of finitely presentable objects in a category. A notion similar to that of accessibility can thus be defined. ------- (3) La tour holomorphe d'une esquisse Cahiers de Top. et de G'eom. Diff. Cat. XXXVII (1996) 295-314 A construction of Lair's in the category of sketches is revisited and noticed to specialize to the construction of the holomorph when restricted to groups. The iteration of this construction reveals two invariants of a sketch: an ordinal and a group. Some explicit computations are provided. ------- (4) Cat'egories accessibles `a produits fibr'es (preprint) Continuation of (1). Accessible categories with (finite) pullbacks are characterized in terms of sketches. This is achieved by introducing "free" colimits in Set: such colimits are proved to be exactly those that commute with pullbacks. ------- (5) Limites projectives conditionnelles dans les cat'egories accessibles (preprint) For fixed b, those b-accessible categories s.t. every diagram with a cone has a limit are characterized in terms of sketches. As a corollary, the category of these categories is Cartesian closed. Similarly for those b-accessible categories s.t. every non-empty diagram with a cone has a limit, or for those with "consistent wide pullbacks". ------- PIERRE AGERON 1) coordonnees bureau adresse : mathematiques, Universite de Caen, 14032 Caen Cedex telephone : 02 31 56 57 37 telecopie : 02 31 93 02 53 adresse electronique : ageron@math.unicaen.fr 2) coordonnees domicile adresse : 28 rue de Formigny 14000 Caen telephone : 02 31 84 39 67