Lecture Notes in Mathematics

From Objects to Diagrams for Ranges of Functors

Authors: Gillibert, Pierre, Wehrung, Friedrich

  • The book is centered on two statements: namely, CLL, and its main precursor, the Armature Lemma, which are results of category theory, with hard proofs, which appear here for the first time. Most of the book is aimed at applications outside category theory, and is thus written as a toolbox.
  • The results of the book illustrate how certain representation problems have counterexamples of different cardinalities such as aleph zero, one, two, and explain why.
  • CLL and the Armature Lemma have a wide application range, which we illustrate with examples in lattice theory, universal algebra, and ring theory. We also give pointers to solutions, made possible by our results, to previously intractable representation problems, with respect to various functors.
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About this book

This work introduces tools from the field of category theory that make it possible to tackle a number of representation problems that have remained unsolvable to date (e.g. the determination of the range of a given functor). The basic idea is: if a functor lifts many objects, then it also lifts many (poset-indexed) diagrams.

Table of contents (1 chapters)

  • Larders from Von Neumann Regular Rings

    Pierre Gillibert, Friedrich Wehrung

    Pages 131-138

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-642-21774-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-642-21773-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
From Objects to Diagrams for Ranges of Functors
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2029
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-21774-6
DOI
10.1007/978-3-642-21774-6
Softcover ISBN
978-3-642-21773-9
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 158
Number of Illustrations and Tables
19 b/w illustrations
Topics