The additivity of traces in triangulated categories
J.P. May
University of Chicago
may@math.uchicago.edu

This paper is a much expanded version of the Appendix of the 
previously posted paper entitled "Picard groups, Grothendieck 
rings, and Burnside rings of categories. In it, we explain a 
fundamental additivity theorem for Euler characteristics and 
generalized trace maps in triangulated categories. The proof 
depends on a refined axiomatization of symmetric monoidal 
categories with a compatible triangulation. The refinement 
consists of several new axioms relating products and 
distinguished triangles. The axioms hold in the examples and 
shed light on generalized homology and cohomology theories.