Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an