Shape Theory: Categorical Methods of Approximation (Dover Books on Mathematics)

Cordier, J. M.; Porter, T.; Mathematics

ISBN 10: 048646623X / ISBN 13: 9780486466231

Editore: Dover Publications, 2008

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Titolo: Shape Theory: Categorical Methods of ...

Casa editrice: Dover Publications

Data di pubblicazione: 2008

Legatura: Paperback

Condizione: New

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Riassunto:

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 and numerable covers, in addition to Morita's form of shape theory. Subsequent chapters explore Bénabou's theory of distributors, the theory of exact squares, Kan extensions, the notion of a stable object, and stability in an Abelian context. The text concludes with a brief description of derived functors of the limit functor theory?the concept that leads to movability and strong movability of systems?and illustrations of the equivalence of strong movability and stability in many contexts.

Contenuti:

Introduction Advice to the reader 1. Borsuk's shape theory for compact metric spaces 2. Categorical shape theory 3. Shape theory for topological spaces 4. Distributors and shape theory 5. Functors between shape theories 6. Stability and movability Appendix: Categorical shape theory and Pattern Recognition, a possible link References Index