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It is then natural to wonder what happens in the category of crossed modules where fiberwise localization is not always available. In this article, we establish an equivalence between conditional flatness and admissibility in the sense of Galois (for the class of regular epimorphisms) for regular-epi localization functors. We use this equivalence to prove that nullification functors are admissible for the class of regular epimorphisms, even if the kernels of their localization morphisms are not acyclic.<\/jats:p>","DOI":"10.1007\/s10485-023-09738-9","type":"journal-article","created":{"date-parts":[[2023,9,8]],"date-time":"2023-09-08T05:01:44Z","timestamp":1694149304000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Admissibility of Localizations of Crossed Modules"],"prefix":"10.1007","volume":"31","author":[{"given":"Olivia","family":"Monjon","sequence":"first","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]},{"given":"J\u00e9r\u00f4me","family":"Scherer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]},{"given":"Florence","family":"Sterck","sequence":"additional","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,9,8]]},"reference":[{"key":"9738_CR1","doi-asserted-by":"crossref","unstructured":"Borceux, F., Bourn, D.: Mal\u2019cev, protomodular, homological and semi-abelian categories. 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