Algebraic approaches to graph transformation. Part I: basic concepts and double pushout approach
Handbook of graph grammars and computing by graph transformation
Towards Secrecy for Rewriting in Weakly Adhesive Categories
Electronic Notes in Theoretical Computer Science (ENTCS)
Van Kampen colimits as bicolimits in span
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Unfolding grammars in adhesive categories
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
ICGT'06 Proceedings of the Third international conference on Graph Transformations
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It is a known fact that the subobjects of an object in an adhesive category form a distributive lattice. Building on this observation, in the paper we show how the representation theorem for finite distributive lattices applies to subobject lattices. In particular, we introduce a notion of irreducible object in an adhesive category, and we prove that any finite object of an adhesive category can be obtained as the colimit of its irreducible subobjects. Furthermore we show that every arrow between finite objects in an adhesive category can be interpreted as a lattice homomorphism between subobject lattices and, conversely, we characterize those homomorphisms between subobject lattices which can be seen as arrows.