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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

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 \(s_2: S\to I_2\), and
2) two such pairs of morphisms are connected by a zig-zag of pairs of such morphisms.

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
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References:

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