Friedrich Wehrung Livres

The book presents a novel universal algebraic approach that connects Tarski's theory of equidecomposability types monoids with abstract measure theory and nonstable K-theory of rings. It introduces a monoid invariant known as the type monoid, explored through Boolean inverse semigroups. The author contrasts these techniques with existing topological methods, offering numerous positive results alongside counterexamples to enrich the understanding of these mathematical concepts.

"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."--Page 4 of cover.