Category Theory in Physics, Mathematics, and Philosophy

• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Kuś, Marek (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt), Skowron, Bartłomiej (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Έκδοση: 1st ed. 2019.
• Σειρά: Springer Proceedings in Physics, 235
• Θέματα: Physics.; Category theory (Mathematics).; Homological algebra.; Mathematics-Philosophy.; Quantum physics.; Mathematical physics.; Mathematical Methods in Physics.; Category Theory, Homological Algebra.; Philosophy of Mathematics.; Quantum Physics.; Mathematical Physics.

 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. 

 Introduction -- Why Categories? -- Category Theory and Philosophy -- Comments on: Category Theory and Philosophy by Zbigniew Krol -- Are There Category-Theoretical Explanations of Physical Phenomena? -- The Application of Category Theory to Epistemic and Poietic Processes -- Asymmetry of Cantorian Mathematics from a Categorial Standpoint: Is It Related to the Direction of Time? -- Extending List's Levels -- From quantum-mechanical lattice of projections to smooth structure of R4 -- Beyond the Space-Time Boundary -- Aspects of Perturbative Quantum Gravity on Synthetic Spacetimes -- Category Theory as a Foundation for the Concept Analysis of Complex Systems and Time Series.