Symmetries and Morphisms

Summary

After having introduced the objects of local theory, their relations are discussed and formalized. Thereby, symmetry is a key concept—however in its modern version which by far exceeds traditional axial or rotational symmetries. The core process of symmetry leads to structure-conserving transformations which we rebuild in the context of local compositions and the underlying forms.

Hoffentlich habe ich diejenigen beschwichtigt, die ein gewisses Unbehagen vor dem Worte Symmetrie, das zu phantasievollen Spekulationen Anlaβ gegeben hat, nicht verbergen kÖnnen, die darin Formalismus, Schematisums sehen und es am liebsten ganz aus der ‘gÖttlichen’ Vernunft verbannen mÖchten.

Wolfgang Graeser [387]