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From Objects to Diagrams for Ranges of Functors [electronic resource] / by Pierre Gillibert, Friedrich Wehrung.

By: Gillibert, Pierre [author.].
Contributor(s): Wehrung, Friedrich [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Lecture Notes in Mathematics: 2029Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011Description: CLVIII, 10p. 19 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783642217746.Subject(s): Mathematics | Algebra | K-theory | Logic, Symbolic and mathematical | Mathematics | Algebra | Category Theory, Homological Algebra | General Algebraic Systems | Order, Lattices, Ordered Algebraic Structures | Mathematical Logic and Foundations | K-TheoryDDC classification: 512 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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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.

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.

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