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.