@inproceedings{BEGG10,
Title = {Finitary M-Adhesive Categories},
Author = {Braatz, B. and Ehrig, H. and Gabriel, K. and Golas, U.},
Booktitle = {Proceedings of Intern. Conf. on Graph Transformation ( ICGT' 10)},
Pages = {234--249},
Year = {2010},
Isbn = {ISBN 978-3-642-15927-5},
Volume = {6372},
Editor = {Ehrig, H. and Rensink, A. and Rozenberg, G. and Sch\"urr, A.},
Publisher = {SPRINGER},
Series = {LNCS},
Abstract = {Finitary M-adhesive categories are M-adhesive categories with finite objects only, where the notion M-adhesive category is short for weak adhesive high-level replacement (HLR) category. We call an object finite if it has a finite number of M-subobjects. In this paper, we show that in finitary M-adhesive categories we do not only have all the well-known properties of M-adhesive categories, but also all the additional HLR-requirements which are needed to prove the classical results for M-adhesive systems. These results are the Local Church-Rosser, Parallelism, Concurrency, Embedding, Extension, and Local Confluence Theorems, where the latter is based on critical pairs. More precisely, we are able to show that finitary M-adhesive categories have a unique E-M-factorization and initial pushouts, and the existence of an M-initial object implies in addition finite coproducts and a unique E0-M0-pair factorization. Moreover, we can show that the finitary restriction of each M-adhesive category is a finitary M-adhesive category and finitariness is preserved under functor and comma category constructions based on M-adhesive categories. This means that all the classical results are also valid for corresponding finitary M-adhesive systems like several kinds of finitary graph and Petri net transformation systems. Finally, we discuss how some of the results can be extended to non-M-adhesive categories.},
Url = {http://tfs.cs.tu-berlin.de/publikationen/Papers10/BEGG10.pdf}
}