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From Objects to Diagrams for Ranges of Functors

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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.

Author(s): Pierre Gillibert, Friedrich Wehrung (auth.)
Series: Lecture Notes in Mathematics 2029
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2011

Language: English
Pages: 158
Tags: Algebra; Category Theory, Homological Algebra; General Algebraic Systems; Order, Lattices, Ordered Algebraic Structures; Mathematical Logic and Foundations; K-Theory

Front Matter....Pages i-x
Background....Pages 1-34
Boolean Algebras That Are Scaled with Respect to a Poset....Pages 35-50
The Condensate Lifting Lemma (CLL)....Pages 51-79
Getting Larders from Congruence Lattices of First-Order Structures....Pages 81-116
Congruence-Permutable, Congruence-Preserving Extensions of Lattices....Pages 117-129
Larders from Von Neumann Regular Rings....Pages 131-138
Discussion....Pages 139-141
Back Matter....Pages 143-158