Abstract
This article shows that symmetry groups as well as broken symmetry groups in natural and abstract mathematical may be used as models of development and evolution objects while describing the states and transformations of such systems. It also demonstrates “visualization” methods of PbTe nanostructures, ZN arithmetic, Galois group for the roots of a fourth degree polynomial, and DNA structure in the framework of category theory.
Highlights
The mathematical models related to category theory are found increasingly necessary in research of natural systems, objects and their structures in the process of growth and development [1]
Any commutative diagram is a directed graph which vertices contain objects, the arrows are morphisms, and the result of the composition of the arrows does not depend on the chosen path
The constructing of composition tables for the elements of symmetry groups and broken symmetry groups is a necessary element of preliminary “digitization” of information
Summary
The mathematical models related to category theory are found increasingly necessary in research of natural systems, objects and their structures in the process of growth and development [1]. Any commutative diagram is a directed graph which vertices contain objects, the arrows are morphisms, and the result of the composition of the arrows does not depend on the chosen path. The structures of directed graphs perform role of commutative diagrams in our studies of symmetry groups (SGrp) and broken symmetry groups (BSGrp). These graphs are shown as the multitude of vertices (points) – structural elements, and morphisms (transformations) are shown as the arrows. Systems’s representing using category theory allows one to calculate the number of their elements, and to visualize in diagrams and directed graphs. The space where we will perform the subsequent visualization of abstract operations for the elements we call the “space of possibilities”
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
