Lair, C. On the class of sketchability of modelizable (accessible) categories with products of two. (Sur le genre d’esquissabilité des catégories modelables (accessibles) possédant les produits de deux.) (French) Zbl 0899.18003 Diagrammes 35, 25-52 (1996). The modelizable categories used in the paper are also called sketchable categories or accessible categories. The modelizable categories which have binary products of objects are characterized up to an equivalence of categories. They are proved to be the categories of models in \({\mathcal S}et\) of some small sketch whose distinguished co-cones have an index category \({\mathcal I}\) satisfying the following property: for any pair of objects \(I_1, I_2\) of \({\mathcal I}\),1) there exists some pair of morphisms of \({\mathcal I}\) with common domain \(s_1: S\to I_1\), and \(s_2: S\to I_2\), and2) two such pairs of morphisms are connected by a zig-zag of pairs of such morphisms. Reviewer: Y.Diers (Faches-Thumesnil) Cited in 12 Documents MSC: 18B99 Special categories 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) 18A10 Graphs, diagram schemes, precategories 18A25 Functor categories, comma categories Keywords:modelizable categories; sketchable categories; accessible categories; binary products × Cite Format Result Cite Review PDF Full Text: EuDML References: [1] C. Lair. Catégories modelables et catégories esquissables. Diagrammes 6, Paris. 1981. Zbl0522.18008 MR684535 · Zbl 0522.18008 [2] R. Guitart et C. Lair. Calcul des modèles syntaxiques et calcul des formules internes. Diagrammes 4, Paris, 1980. Zbl0508.03030 · Zbl 0508.03030 [3] C. Lair. Catégories qualifiables et catégories esquissables. Diagrammes 17. Paris. 1987. Zbl0624.18003 MR918001 · Zbl 0624.18003 [4] C. Lair. Diagrammes localement libres, extensions de corps et théorie de Galois. Diagrammes 10. Paris, 1983. Zbl0569.18001 MR780448 · Zbl 0569.18001 [5] C. Ehresmann. Esquisses et types des structures algébriques. Bul. Instit. Polit. Iasi. XIV. 1968. Zbl0196.03102 · Zbl 0196.03102 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.