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The main results show that processes are in one-to-one correspondence with switch-equivalent classes of derivations, and that the unfolding construction can be characterised as a coreflection, that is, the unfolding functor arises as the right adjoint to the embedding of the category of occurrence grammars into the category of grammars.<\/jats:p><jats:p>As the unfolding represents potentially infinite computations, we need to work in adhesive categories with \u2018well-behaved\u2019 colimits of \u03c9-chains of monos. Compared with previous work on the unfolding of Petri nets and graph grammars, our results apply to a wider class of systems, which is due to the use of a refined notion of grammar morphism.<\/jats:p>","DOI":"10.1017\/s096012951200031x","type":"journal-article","created":{"date-parts":[[2014,6,26]],"date-time":"2014-06-26T14:22:13Z","timestamp":1403792533000},"source":"Crossref","is-referenced-by-count":3,"title":["Processes and unfoldings: concurrent computations in adhesive categories"],"prefix":"10.1017","volume":"24","author":[{"given":"PAOLO","family":"BALDAN","sequence":"first","affiliation":[]},{"given":"ANDREA","family":"CORRADINI","sequence":"additional","affiliation":[]},{"given":"TOBIAS","family":"HEINDEL","sequence":"additional","affiliation":[]},{"given":"BARBARA","family":"K\u00d6NIG","sequence":"additional","affiliation":[]},{"given":"PAWE\u0141","family":"SOBOCI\u0143SKI","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,6,26]]},"reference":[{"key":"S096012951200031X_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2008.04.002"},{"key":"S096012951200031X_ref38","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0055644"},{"key":"S096012951200031X_ref25","unstructured":"Heindel T. (2009) A Category Theoretical Approach to the Concurrent Semantics of Rewriting: Adhesive Categories and Related Concepts, Ph.D. thesis, Universit\u00e4t Duisburg-Essen."},{"key":"S096012951200031X_ref35","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-3190-6"},{"key":"S096012951200031X_ref17","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0025714"},{"key":"S096012951200031X_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(87)90124-1"},{"key":"S096012951200031X_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2009.11.009"},{"key":"S096012951200031X_ref15","doi-asserted-by":"crossref","first-page":"241","DOI":"10.3233\/FI-1996-263402","article-title":"Graph processes.","volume":"26","author":"Corradini","year":"1996","journal-title":"Fundamenta Informaticae"},{"key":"S096012951200031X_ref12","unstructured":"Cockett R. and Guo X. (2007) Join restriction categories and the importance of being adhesive. 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(2000) Modelling Concurrent Computations: from Contextual Petri Nets to Graph Grammars, Ph.D. thesis, Dipartimento di Informatica, Universit\u00e0 di Pisa."},{"key":"S096012951200031X_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s10485-008-9127-6"},{"key":"S096012951200031X_ref7","doi-asserted-by":"publisher","DOI":"10.1006\/inco.2001.3060"},{"key":"S096012951200031X_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/11690634_14"},{"key":"S096012951200031X_ref20","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129500001353"},{"key":"S096012951200031X_ref37","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(88)90034-X"},{"key":"S096012951200031X_ref18","volume-title":"Fundamentals of Algebraic Graph Transformation","author":"Ehrig","year":"2006"},{"key":"S096012951200031X_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2006.11.004"},{"key":"S096012951200031X_ref30","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73859-6_21"},{"key":"S096012951200031X_ref24","unstructured":"Hayman J. and Winskel G. 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