The Additivity of Traces in Triangulated Categories

  title={The Additivity of Traces in Triangulated Categories},
  author={John P. May},
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. 
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