This in-depth treatment uses shape theory as a "case study" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras.
A short introduction to geometric shape explains specifics of the construction of the shape category and relates it to an abstract definition of shape theory. Upon returning to the geometric base, the text considers simplical complexes...