From Objects to Diagrams for Ranges of Functors

ISBN-13: 9783642217739 / Angielski / Miękka / 2011 / 158 str.

Pierre Gillibert;Friedrich Wehrung

Opis

Introduces tools, from the field of category theory, that make it possible to tackle representation problems (determination of the range of a given functor).

Spis treści

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.

Blurb

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.