Unifying Exact Completions

We define the notion of exact completion with respect to an existential elementary doctrine. We observe that the forgetful functor from the 2category 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. MSC 2000: 03G30 03B15 18C50 03B20 03F55

• Type: Journal
• Year: 2015
• Where: ACS
• Authors: Maria Emilia Maietti, Giuseppe Rosolini
• Keywords: ACS 2015, Distributed And Parallel Computing