From Objects to Diagrams for Ranges of Functors

This work introduces tools, from the field of category theory, that make it possible to tackle until now unsolvable representation problems (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.

List of contents

1 Background.- 2 Boolean Algebras Scaled with Respect to a Poset.- 3 The Condensate Lifting Lemma (CLL).- 4 Larders from First-order Structures.- 5 Congruence-Preserving Extensions.- 6 Larders from von Neumann Regular Rings.- 7 Discussion.

Summary

This work introduces tools, from the field of category theory, that make it possible to tackle until now unsolvable representation problems (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.

Product details

• Authors: Pierr Gillibert, Pierre Gillibert, Friedrich Wehrung
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.08.2011
• EAN: 9783642217739
• ISBN: 978-3-642-21773-9
• No. of pages: 158
• Dimensions: 158 mm x 234 mm x 11 mm
• Weight: 272 g
• Illustrations: X, 158 p. 19 illus.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra