A central concept in algebraic topology since the 1970's has been that of delooping machine [4] [23] [29]. Such a " machine " corresponds to a notion of H-space, or space with a multiplication satisfying associativity, unity and inverse properties up to homotopy in an appropriate way, including higher order coherences as first investigated in [33]. A delooping machine is a specification of the ...

We present a new approach to rewriting obtained by enhancing and unifying existing variants inside the algebraic (or better categorical) approach to (graph) rewriting. Our approach is motivated by second-order term graph rewriting and stresses on one hand the two-step nature of rule application consisting of deleting and adding items and on the other hand the heterogeneous nature of the rewriti...

A distributed graph (N, D) consists of a network graph N and a commutative diagram D over the scheme N which associates local graphs D(ni) and graph morphisms D(e) : D(n1) → D(n2) to nodes n1, n2 and edges e : n1 → n2 in N . Although there are several interesting applications of distributed graphs and transformations, even the basic pushout constructions for the double pushout approach of distr...

We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved. Many types of graphical structures used in computer science are shown to be examples of adhesive categories. Double-pushout graph rewriting generalises well to rewriting on arbitrary adhesive categories.

We show how graph rewriting can be described with a single pushout in a suitable category of graphs, and compare our result with the conventional approach which uses double pushouts.

In this paper we investigate and compare four variants of the double-pushout approach to graph transformation. As well as the traditional approach with arbitrary matching and injective right-hand morphisms, we consider three variations by employing injective matching and/or arbitrary right-hand morphisms in rules. We show that injective matching provides additional expressiveness in two respect...

The paper extends Sesqui-Pushout Graph Rewriting (SqPO) by polymorphism, a key concept in object-oriented design. For this purpose, the necessary theory for rule composition and decomposition is elaborated on an abstract categorical level. The results are applied to model rule extension and type dependent rule application. This extension mechanism qualifies SqPO – with its very useful copy mech...

We prove cocompleteness of the category of CASL signatures , of monotone signatures, of strongly regular signatures and of strongly locally ltered signatures. This shows that using these signature categories is compatible with a pushout or colimit based module system.