Our main results concerning this construction are real versions of the group-completion theorem and the additivity theory, stated in the introduction as Theorem A and Theorem B, respectively. We stress that all theorems in the book, including Theorem A and Theorem B, are valid also if 2 is not invertible in the hom-abelian groups of *C*.

A word of warning is in order. The book is in preliminary form and, at present, only contains a full proof of Theorem A. There are also some inconsistencies stemming from the two possible choices of how to view a partially ordered set as a category.

- book.pdf [April 17, 2015]

Lars Hesselholt <larsh@math.nagoya-u.ac.jp>