{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:27Z","timestamp":1753894407420,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,6]]},"abstract":"<jats:p>Adhesive and quasiadhesive categories provide a general framework for the study of algebraic graph rewriting systems. In a quasiadhesive category any two regular subobjects have a join which is again a regular subobject. Vice versa, if regular monos are adhesive, then the existence of a regular join for any pair of regular subobjects entails quasiadhesivity. It is also known (quasi)adhesive categories can be embedded in a Grothendieck topos via a functor preserving pullbacks and pushouts along (regular) monomorphisms. In this paper we extend these results to $\\mathcal{M}, \\mathcal{N}$-adhesive categories, a concept recently introduced to generalize the notion of (quasi)adhesivity. We introduce the notion of $\\mathcal{N}$-adhesive morphism, which allows us to express $\\mathcal{M}, \\mathcal{N}$-adhesivity as a condition on the subobjects' posets. Moreover, $\\mathcal{N}$-adhesive morphisms allows us to show how an $\\mathcal{M},\\mathcal{N}$-adhesive category can be embedded into a Grothendieck topos, preserving pullbacks and $\\mathcal{M}, \\mathcal{N}$-pushouts.<\/jats:p>","DOI":"10.46298\/lmcs-21(1:22)2025","type":"journal-article","created":{"date-parts":[[2025,3,6]],"date-time":"2025-03-06T09:20:06Z","timestamp":1741252806000},"source":"Crossref","is-referenced-by-count":0,"title":["On The Axioms Of $\\mathcal{M},\\mathcal{N}$-Adhesive Categories"],"prefix":"10.46298","volume":"Volume 21, Issue 1","author":[{"given":"Davide","family":"Castelnovo","sequence":"first","affiliation":[]},{"given":"Marino","family":"Miculan","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2025,3,6]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/15333\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/15333\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,6]],"date-time":"2025-03-06T09:20:07Z","timestamp":1741252807000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/12930"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,6]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-21(1:22)2025","relation":{"has-preprint":[{"id-type":"arxiv","id":"2401.12638v5","asserted-by":"subject"},{"id-type":"arxiv","id":"2401.12638v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2401.12638v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2401.12638","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2401.12638","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2025,3,6]]},"article-number":"12930"}}