Equivalences, partitions and (bi)simulations are usually tackled using concrete relations. There are only few treatments by abstract relation algebra or category theory. We give an approach based on the theory of semirings and quantales. This allows applying the results directly to structures such as path and tree algebras which is not as straightforward in the other approaches mentioned. Also,...

The paper aims to demonstrate that category theory (CT) methods are appropriate in the model management context. We show that CT naturally appears on stage, when we model such basic constructs as model merge and parallel composition accurately and consistently. We present categorical constructs in a tutorial-like style by applying them to simple labeled transition systems (LTSs), and reveal new...

We consider two related approaches to quantizing general relativity which involve replacing point set topology with category theory as the foundation for the theory. The ideas of categorical topology are introduced in a way we hope is physicist friendly.

In order to apply nonstandard methods to modern algebraic geometry, as a first step in this paper we study the applications of nonstandard constructions to category theory. It turns out that many categorical properties are well behaved under enlargements.

The concept of information has found application across the sciences. However, the conventional measures of information are not appropriate for all situations, and a more general mathematical concept is needed. In this work we give axioms that characterize the arithmetic of information, i.e. the way that pieces of information combine with each other. These axioms allow for a general notion of i...

Category theory was formalized in Mizar with two different approaches [7], [18] that correspond to those most commonly used [16], [5]. Since there is a one-to-one correspondence between objects and identity morphisms, some authors have used an approach that does not refer to objects as elements of the theory, and are usually indicated as object-free category [1] or as arrowsonly category [16]. ...

The centrality of the whole/part relation in mathematics is demonstrated through the presentation and analysis of examples from algebra, geometry, functional analysis, logic, topology and category theory.

We have systems rich in information but poor in knowledge. The paper shall sketch a framework in which information and knowledge could be properly integrated. Our initial hypothesis is that passing from information to knowledge involves the elaboration of a well structured theory of semiotic units. The latter is codified by a three-fold structure: an expression, a content and an ontological com...

We are developing a new software methodology for building large, complicated systems out of simple units. In this paper, we describe application of aa orglmic progr~mrniug to multi-agent systems. One of the advantages resides in that we can program the system in a subsumptive manner.

Although the contribution of Category Theory as a mathematical platform for supporting software development, in the wake of Goguen’s approach to General Systems, is now reasonably recognised, accepted and even used, the emergence of new modelling techniques and paradigms associated with the “New-Economy” suggests that the whole approach needs to be revisited. In this paper, we propose some revi...