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This framework provides a natural setting for extending certain classical results in algebra. We study the fundamental properties of prenormal categories, including a characterisation in terms of a factorisation system involving normal epimorphisms, and a categorical version of Noether\u2019s so-called \u2018third isomorphism theorem\u2019. We also present a range of examples, with the category of commutative monoids constituting a central one. In the second part of the paper we extend prenormality and its related properties to the non-pointed context, using kernels and cokernels defined relative to a distinguished class of trivial objects.\n                  <\/jats:p>","DOI":"10.1007\/s10485-025-09835-x","type":"journal-article","created":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T14:41:10Z","timestamp":1766500870000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Prenormal Categories"],"prefix":"10.1007","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7941-1851","authenticated-orcid":false,"given":"Sandra","family":"Mantovani","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0004-0848-6241","authenticated-orcid":false,"given":"Mariano","family":"Messora","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,12,23]]},"reference":[{"key":"9835_CR1","unstructured":"Ad\u00e1mek, J., Herrlich, H., Strecker, G.: Abstract and concrete categories: the joy of cats. 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