Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.
You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.
After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.
The book is centered on two statements: namely, CLL, and its main precursor, the Armature Lemma, which are results of category theory, with hard proofs, which appear here for the first time. Most of the book is aimed at applications outside category theory, and is thus written as a toolbox.
The results of the book illustrate how certain representation problems have counterexamples of different cardinalities such as aleph zero, one, two, and explain why.
CLL and the Armature Lemma have a wide application range, which we illustrate with examples in lattice theory, universal algebra, and ring theory. We also give pointers to solutions, made possible by our results, to previously intractable representation problems, with respect to various functors.
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.