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Unifying exact completions
Published 5 Dec 2012 in math.CT, cs.LO, and math.LO | (1212.0966v1)
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 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 cartesian category with weak pullbacks.
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