Accessible categories with non-empty projective limits and accessible categories with finite projective limits. (Catégories accessibles à limites projectives non vides et catégories accessibles à limites projectives finies.) (French) Zbl 0873.18002

The paper gives characterizations of accessible categories which have non empty limits, or finite limits, or non empty finite limits, or finite connected limits, in terms of categories of models in \({\mathcal S}et\) of some particular sketches. For example, a category is \(\beta\)-accessible with non empty limits if and only if it is equivalent to the category of models of some sketch whose projective cones are \(\beta\)-small and inductive cones are empty. A category is accessible with finite limits if and only if it is equivalent to the category of models of a sketch whose inductive cones are filtered.


18A25 Functor categories, comma categories
18A35 Categories admitting limits (complete categories), functors preserving limits, completions
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