From Objects to Diagrams for Ranges of Functors

• Main Authors: Gillibert, Pierre (Author), Wehrung, Friedrich (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Series: Lecture Notes in Mathematics, 2029
• Subjects: Mathematics.; Algebra.; Category theory (Mathematics).; Homological algebra.; K-theory.; Ordered algebraic structures.; Mathematical logic.; Category Theory, Homological Algebra.; General Algebraic Systems.; Order, Lattices, Ordered Algebraic Structures.; Mathematical Logic and Foundations.; K-Theory.

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...

Table 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.