Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-6438
|Main Title:||Finitary M-adhesive categories|
|Abstract:||Finitary M-adhesive categories are M-adhesive categories with finite objects only, where M-adhesive categories are a slight generalisation of weak adhesive high-level replacement (HLR) categories. We say an object is finite if it has a finite number of M-subobjects. In this paper, we show that in finitary M-adhesive categories we not only have all the well-known HLR properties of weak adhesive HLR categories, which are already valid for M-adhesive categories, but also all the additional HLR requirements needed to prove classical results including the Local Church-Rosser, Parallelism, Concurrency, Embedding, Extension and Local Confluence Theorems, where the last of these is based on critical pairs. More precisely, we are able to show that finitary M-adhesive categories have a unique ε'-M factorisation and initial pushouts, and the existence of an M-initial object implies we also have finite coproducts and a unique ε' -M pair factorisation. Moreover, we can show that the finitary restriction of each M-adhesive category is a finitary M-adhesive category, and finitarity 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 transformation systems including 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.|
|DDC Class:||004 Datenverarbeitung; Informatik|
|Journal Title:||Mathematical structures in computer science|
|Publisher:||Cambridge University Press|
|Notes:||Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.|
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
|Appears in Collections:||Inst. Softwaretechnik und Theoretische Informatik » Publications|
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