An Elementary Introduction to n-fold Groupoids

Groupoids and n-fold groupoids unify and generalize the concepts of local symmetries (groups) and distant symmetries of various kinds as they manifest themselves in physical systems. The available mathematical treatments of these topics appear mostly in highly specialized journals and monographs. The aim of this book is to expose the non-specialist to these ideas and to contextualize them within the concrete framework of applications to solid mechanics, such as composite materials and metamaterials. No previous background is assumed in either the theory or the applications. In chapters that alternate the treatment of the mathematical underpinnings with their materialization in the response of elastic bodies the reader is invited to undertake a rewarding journey. Examples and exercises are proposed throughout.