### The additivity of traces in triangulated categories, by J. P. May

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.

J. P. May <may@math.uchicago.edu>