The Additivity of Traces in Triangulated Categories

By Jon P. May. 2001

205 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4df88ad8188d98315f044d7eaf76d99f4bd20091

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Citations in the corpus

Magnitude homology of enriched categories and metric spaces (2017, background): “reover, in this case there is a canonical choice of χ: Example 5.3. If W is a stable symmetric monoidal model category, its homotopy category Ho(W) is a monoidal triangulated category in the sense of [May01]. In particular it is additive, so the endomorphisms of the unit object in Ho(W) form a ring,”
Kaplansky classes and derived categories (2007, methodology): “We would also automatically have the additivity property of generalized trace maps as defined in [ 23 ].”
More Concise Algebraic Topology: Localization, Completion, and Model Categories (2012, background): “3 are precursors of another axiom used in the usual definition of triangulated categories, but that axiom is shown to be redundant in [90].”
Hereditary abelian model categories (2015, background): “One benefit of having this monoidal model structure is that it follows at once that the triangulated structure on the homotopy category D(X) is strongly compatible with the derived tensor product; see [46].”
The spectrum of prime ideals in tensor triangulated categories (2004, background): “At the present stage of the theory, we do not need the higher axiomatic of May [11] or Keller and Neeman [9].”
Traces in symmetric monoidal categories (2011, background): “isﬁes many useful naturality properties which we summarize here. We omit most proofs, which are straightforward diagram chases (and are especially easy in string diagram notation). References include [11,24,28,34]. We begin with invariance under dualization. Recall that any f: Q⊗M → M⊗P has a mate f”
The Mukai pairing, I: the Hochschild structure (2003, unknown): “Let X and Y be spaces whose derived categories are equivalent via a FourierMukai transform (i.e., the equivalence is given by an integral transform).”
Derived categories, resolutions, and Brown representability (2005, background): “There is an equivalent formulation of (TR4) due to May which displays the exact triangles in a diagram having the shape of a braid [19].”
Lecture Notes On Motivic Cohomology (2006, background): “Vladimir Voevodsky Institute for Advanced Study May 2001 Introduction This book is divided into six main parts.”
Parametrized homotopy theory (2004, methodology): “The following basic properties of the trace are proven in [59, III§7] and in [74], where more detailed statements are given.”
A modular description of the K(2)-local sphere at the prime 3 (2005, background): “Let (C;^; F ( ; ); S) be a closed symmetric monoidal category with compatible triangulated structure [33].”
Picard Groups, Grothendieck Rings, and Burnside Rings of Categories (2001, background): “There are many generalizations of this example in classical and equivariant stable homotopy theory, and many more in such modern refinements of stable homotopy theory as [9].”