Abstract
We define the notion of exact completion with respect to an existential elementary doctrine. We observe that the forgetful functor from the 2-category of exact categories to existential elementary doctrines has a left biadjoint that can be obtained as a composite of two others. Finally, we conclude how this notion encompasses both that of the exact completion of a regular category as well as that of the exact completion of a category with binary products, a weak terminal object and weak pullbacks.
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Maietti, M.E., Rosolini, G. Unifying Exact Completions. Appl Categor Struct 23, 43–52 (2015). https://doi.org/10.1007/s10485-013-9360-5
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DOI: https://doi.org/10.1007/s10485-013-9360-5