Abstract

Abstract. 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. Contents 1. Generalized trace maps 2 2. Triangulated categories 6 3. Weak pushouts and weak pullbacks 9 4. The compatibility axioms 11

Citations

279	Homotopical Algebra - Quillen - 1967
182	Model categories - Hovey - 1999
124	Algebras and modules in monoidal model categories - Schwede, Shipley
119	Deligne, Faisceaux pervers - Beilinson, Bernstein, et al. - 1982
106	modules, and algebras in stable homotopy theory. With an appendix by M - Rings - 1997
104	Axiomatic stable homotopy theory - Hovey, Palmieri, et al. - 1997
94	Model categories of diagram spectra - Mandell, May, et al.
82	Triangulated Categories - Neeman
61	Algebraic Topology - Homotopy and Homology - Switzer - 1975
56	Homotopy limits in triangulated categories - Bökstedt, Neeman - 1993
36	and with contributions by - Lewis, May, et al. - 1986
27	Stable homotopy and generalized homology - Adams - 1974
16	groups, Grothendieck rings, and Burnside rings of categories, Adv.Math - May, Picard - 2001
13	Some new axioms for triangulated categories - Neeman - 1991
11	Spectra and the Steenrod algebra., North-Holland Mathematical Library, 29. North-Holland Publishing Co - Margolis - 1983
1	Catégories dérivées, in Springer Lecture Notes in Mathematics Vol 569 - Verdier - 1971