Axiomization of Passage from `Local' Structure to `Global' Object

Download or read book Axiomization of Passage from `Local' Structure to `Global' Object written by Paul Feit and published by American Mathematical Soc.. This book was released on 1993 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper offers a systematic approach to all mathematical theories with local/global behavior. To build objects with local and global aspects, on begins with a category of [script]C of allowed local structures, and somehow derives a category [script]C[superscript]gl of things which are 'locally' in [script]C. Some global objects, such as manifolds or schemes, can be represented as a sheaf of algebras on a topological base space; others, like algebraic spaces, are more technical. These theories share common structure--certain theorems on inverse limits, descent, and dependence on special class of morphism appear in all cases. Yet, classical proofs for universal properties proceed by case-by-case study. Separate examples require distinct arguments.