Separability and triangulated categories

By Paul Balmer. 2011

64 citations recorded by the source corpus.

Abstract We prove that the category of modules over a separable ring object in a tensor triangulated category admits a unique structure of triangulated category which is compatible with the original one. This applies in particular to etale algebras. More generally, we do this for exact separable monads.

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

View Paper: https://www.semanticscholar.org/paper/37b52992ab1256935ac4b2cdd1b7ada2d25044a5

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In Algebra and Number Theory

1. A. Elagin
2. Beren Sanders
3. M. Gorsky
4. Paul Balmer
5. M. Schlichting
6. Henning Krause
7. C. Walter
8. P. Seidel

In Geometry and Topology

1. A. Elagin
2. Beren Sanders
3. M. Gorsky
4. Paul Balmer
5. M. Schlichting
6. Greg Stevenson
7. Henning Krause
8. A. Neeman

In Mathematical Physics

1. A. Elagin
2. Beren Sanders
3. M. Gorsky
4. Paul Balmer
5. M. Schlichting
6. Greg Stevenson
7. Henning Krause
8. A. Neeman

Citations in the corpus

• Semi-derived and derived Hall algebras for stable categories (2014, background): “oming sequel of this work. We should say also that the K-theory is a well-defined invariant of a certain strictified version of triangulated categories, called Heller, or ∞−triangulated categories, see [Bal][Ku¨n1][M]. Thisclass coversall algebraic triangulatedcategories. It istherefore possiblethat o”
• Stacks of group representations (2013, methodology): “So, k C p - Stab can be obtained out of k G - Stab and A ℓ by the purely triangulated-categorical method of [Bal11].”
• The axioms for n–angulated categories (2011, unknown): “[1]) of triangulated categories of order n.”
• ON EQUIVARIANT TRIANGULATED CATEGORIES (2014, background): “ [14]. See also G.Maltsiniotis [18]. For any n > 2 they define triangulated categories of order nby introducing distinguished n-triangles. We give the definitions only for n= 2 and 3. Definition 6.2 ([2], Definition 5.11). It is said that a suspended category T with a class of distinguished triangles”
• The spectrum of the equivariant stable homotopy category of a finite group (2015, background): “r every subgroup H ≤ G, the G-spectrum AG H := G/H+ (we often drop the Σ∞ G for readability) is a separable commutative ring object (=a tt-ring, or a finite ´etale ring) in the tt-category SH(G). (See [Bal11] and [Bal13] for the definition of separable and for a discussion of how such rings provide 8 ”