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Collagories for Relational Adhesive Rewriting [chapter]

Wolfram Kahl
2009 Lecture Notes in Computer Science  
Collagories closely correspond to the adhesive categories important for the categorical DPO approach to graph transformation. but thanks to their relation-algebraic flavour provide a more accessible and  ...  We define collagories essentially as "distributive allegories without zero morphisms", and show that they are sufficient for accommodating the relation-algebraic approach to graph transformation.  ...  Maps in Collagories form Adhesive Categories Adhesive categories as a more specific setting for double-pushout graph rewriting have been introduced by Lack and Sobociński [LS04, LS05] ; the following  ... 
doi:10.1007/978-3-642-04639-1_15 fatcat:bm25nypvrzg45d2bujmxtazhse

Co-tabulations, Bicolimits and Van-Kampen Squares in Collagories

Wolfram Kahl
2010 Electronic Communications of the EASST  
Collagories are sufficient for accommodating the relation-algebraic approach to graph transformation, and closely correspond to the adhesive categories important for the categorical DPO approach to graph  ...  Heindel and Sobocinski have recently characterised the Van-Kampen colimits used in adhesive categories as bicolimits in span categories.  ...  Van Kampen Squares in Collagories Adhesive categories as a more specific setting for double-pushout graph rewriting have been introduced by Lack and Sobociński [LS04, LS05] ; the following two definitions  ... 
doi:10.14279/tuj.eceasst.29.421 dblp:journals/eceasst/Kahl10 fatcat:wsvz27337vc2bp7ssiq7j26paa

Collagories: Relation-algebraic reasoning for gluing constructions

Wolfram Kahl
2011 The Journal of Logic and Algebraic Programming  
Typical collagories relevant for generalised graph structure transformation can be obtained from basic collagories like that of sets and relations via nestable constructions of collagories of semi-unary  ...  Since collagories are intended as foundation for generalised graph structure transformation in the algebraic tradition, we concentrate particularly on co-tabulations, the core of the relation-algebraic  ...  categories Adhesive categories and Van Kampen setups Adhesive categories as a more specific setting for double-pushout graph rewriting have been introduced by Lack and Sobociński [18, 19] ; the following  ... 
doi:10.1016/j.jlap.2011.04.006 fatcat:kizotnswyjg63f26fe54l43upa

Graph Rewriting and Relabeling with PBPO+ (Extended Version) [article]

Roy Overbeek, Jörg Endrullis, Aloïs Rosset
2021 arXiv   pre-print
We extend the powerful Pullback-Pushout (PBPO) approach for graph rewriting with strong matching.  ...  In addition, we show that PBPO+ is well-suited for rewriting labeled graphs and certain classes of attributed graphs.  ...  We would also like to thank Michael Shulman, who identified the sufficient conditions for amendability for us [23] .  ... 
arXiv:2010.08230v2 fatcat:x2kpnuufbbb6rcnvvkuzzfbww4

The Pullback-Pushout Approach to Algebraic Graph Transformation [chapter]

Andrea Corradini, Dominque Duval, Rachid Echahed, Frédéric Prost, Leila Ribeiro
2017 Lecture Notes in Computer Science  
The paper is organized as follows: In Section 2, we define pb-po rewriting and in Section 3, we show its relation with the agree and sqpo approaches.  ...  Then, we discuss issues regarding the locality of pb-po rewriting in Section 4. In Section 5,  ...  n g 3 Relating pb-po with agree and sqpo rewriting In this section, we first show that pb-po extends both agree and sqpo with monic matches (in categories where agree rewriting is defined), and then discuss  ... 
doi:10.1007/978-3-319-61470-0_1 fatcat:jpq33uin3jhg3i4iu4mq7774wq