A theorem on barr-exact categories, with an infinitary generalization

Annals of Pure and Applied Logic 47 (3):225-268 (1990)
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Abstract

Let C be a small Barr-exact category, Reg the category of all regular functors from C to the category of small sets. A form of M. Barr's full embedding theorem states that the evaluation functor e : C →[Reg, Set ] is full and faithful. We prove that the essential image of e consists of the functors that preserve all small products and filtered colimits. The concept of κ-Barr-exact category is introduced, for κ any infinite regular cardinal, and the natural generalization to κ-Barr-exact categories of the above result is proved. The treatment combines methods of model theory and category theory. Some applications to module categories are given.

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References found in this work

Strong conceptual completeness for first-order logic.Michael Makkai - 1988 - Annals of Pure and Applied Logic 40 (2):167-215.

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