1,373 research outputs found
Categorical Abstract Rewriting Systems and Functoriality of Graph Transformation
Rewriting systems are often defined as binary relations over a given set of
objects. This simple definition is used to describe various properties of
rewriting such as termination, confluence, normal forms etc. In this paper, we
introduce a new notion of abstract rewriting in the framework of categories.
Then, we define the functoriality property of rewriting systems. This property
is sometimes called vertical composition. We show that most of graph
transformation systems are functorial and provide a counter-example of graph
transformation systems which is not functorial
Universal Constructions for (Co)Relations: categories, monoidal categories, and props
Calculi of string diagrams are increasingly used to present the syntax and
algebraic structure of various families of circuits, including signal flow
graphs, electrical circuits and quantum processes. In many such approaches, the
semantic interpretation for diagrams is given in terms of relations or
corelations (generalised equivalence relations) of some kind. In this paper we
show how semantic categories of both relations and corelations can be
characterised as colimits of simpler categories. This modular perspective is
important as it simplifies the task of giving a complete axiomatisation for
semantic equivalence of string diagrams. Moreover, our general result unifies
various theorems that are independently found in literature and are relevant
for program semantics, quantum computation and control theory.Comment: 22 pages + 3 page appendix, extended version of arXiv:1703.0824
Reconfigurable Decorated PT Nets with Inhibitor Arcs and Transition Priorities
In this paper we deal with additional control structures for decorated PT
Nets. The main contribution are inhibitor arcs and priorities. The first ensure
that a marking can inhibit the firing of a transition. Inhibitor arcs force
that the transition may only fire when the place is empty. an order of
transitions restrict the firing, so that an transition may fire only if it has
the highest priority of all enabled transitions. This concept is shown to be
compatible with reconfigurable Petri nets
Fibrancy of Partial Model Categories
We investigate fibrancy conditions in the Thomason model structure on the
category of small categories. In particular, we show that the category of weak
equivalences of a partial model category is fibrant. Furthermore, we describe
connections to calculi of fractions.Comment: 30 page
Geometrically Partial actions
We introduce "geometric" partial comodules over coalgebras in monoidal
categories, as an alternative notion to the notion of partial action and
coaction of a Hopf algebra introduced by Caenepeel and Janssen. The name is
motivated by the fact that our new notion suits better if one wants to describe
phenomena of partial actions in algebraic geometry. Under mild conditions, the
category of geometric partial comodules is shown to be complete and cocomplete
and the category of partial comodules over a Hopf algebra is lax monoidal. We
develop a Hopf-Galois theory for geometric partial coactions to illustrate that
our new notion might be a useful additional tool in Hopf algebra theory.Comment: revised version; improved presentation; stronger version of
"fundamental theorem" for partial comodules. Version accepted for publication
in "Transactions of the American Mathematical Society". Updated reference
Subtyping for Hierarchical, Reconfigurable Petri Nets
Hierarchical Petri nets allow a more abstract view and reconfigurable Petri
nets model dynamic structural adaptation. In this contribution we present the
combination of reconfigurable Petri nets and hierarchical Petri nets yielding
hierarchical structure for reconfigurable Petri nets. Hierarchies are
established by substituting transitions by subnets. These subnets are
themselves reconfigurable, so they are supplied with their own set of rules.
Moreover, global rules that can be applied in all of the net, are provided
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