The contributions gathered here demonstrate how categorical ontology can provide a basis for linking three important basic sciences: mathematics, physics, and philosophy. Category theory is a new formal ontology that shifts the main focus from objects to processes.

The book approaches formal ontology in the original sense put forward by the philosopher Edmund Husserl, namely as a science that deals with entities that can be exemplified in all spheres and domains of reality. It is a dynamic, processual, and non-substantial ontology in which all entities can be treated as transformations, and in which objects are merely the sources and aims of these transformations.

Thus, in a rather surprising way, when employed as a formal ontology, category theory can unite seemingly disparate disciplines in contemporary science and the humanities, such as physics, mathematics and philosophy, but also computer and complex systems science.

Table of Contents

1 Why Categories?

2 Category Theory and Philosophy

3 Are There Category-Theoretical Explanations of Physical Phenomena?

4 The Application of Category Theory to Epistemic and Poietic Processes

5 Asymmetry of Cantorian Mathemat ics from a Categorial Standpoint: Is It Related to the Direction of Time?

6 Extending List's Levels

7 From Quantum-Mechanical Lattice of Projections to Smooth Structure of mathbbR4

8 Beyond the Space-Time Boundary

9 Aspects of Perturbative Quantum Gravity on Synthetic Spacetimes

10 Category Theory as a Foundation for the Concept Analysis of Complex Systems and Time Series

About the Authors

Prof. Dr. Marek Kus is a theoretical physicis, professor at the Centre of Theoretical Physics of the Polish Academy of Sciences in Warsaw, Director of the International Center for Formal Ontology at the Faculty of Administration and Social Sciences of the Warsaw University of Technology, member of Academia Europea. His scientific interests include:mathematical physics, in particular the application of geometric and group-theoretic methods (simplectic geometry, algebraic geometry, Lie group theory) in quantum computer science, quantum chaos and the basics of quantum mechanics. He is also interested in formal methods in philosophy and the application of methods of exact sciences in social sciences. He is the author of over 150 original articles.

Dr. Bartłomiej Skowron is a Platonic philosopher. He wrote his Ph.D. thesis on Mereotopological aspects of philosophical part-whole theory at the University of Wroclaw, and defended his thesis in 2012. He received also BA in Mathematics from the University of Wroclaw, Faculty of Mathematics and Computer Science, in 2011. From October2015, he is an assistant professor at the Faculty of Administration and Social Sciences at the Warsaw University of Technology. He is a member of the International Center for Formal Ontology and the Academyof Young Scholars and Artists. He served as a President of the Academy from 2013 to 2017. His main research interest is in Mathematical (especially Topological) Philosophy. He is laso interested in formal ontology (part-whole theory, mereotopology), phenomenology, philosophy of morality, axiology, philosophical anthropology, the basis and philosophy of mathematics, applied logic and applied topology.He has edited or is currently editing 7 books. He is the author of over 30 original articles.