From Objects to Diagrams for Ranges of Functors - Gillibert, Pierre; Wehrung, Friedrich; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg, 2011)
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.
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.
Keywords: 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-Theory.