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Main Title: Finitary M-adhesive categories
Author(s): Gabriel, Karsten
Braatz, Benjamin
Ehrig, Hartmut
Golas, Ulrike
Type: Article
Language Code: en
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.
Issue Date: 2014
Date Available: 23-Nov-2017
DDC Class: 004 Datenverarbeitung; Informatik
Journal Title: Mathematical structures in computer science
Publisher: Cambridge University Press
Publisher Place: Cambridge
Volume: 24
Issue: 4
Article Number: e240403
Publisher DOI: 10.1017/s0960129512000321
EISSN: 1469-8072
ISSN: 0960-1295
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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