From Objects to Diagrams for Ranges of Functors

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.