Comparison of abelian categories recollements

By V. Franjou, T. Pirashvili. Documenta Mathematica, 2004

128 citations recorded by the source corpus.

We give a necessary and sufficient condition for a mor- phism between recollements of abelian categories to be an equivalence. 2000 Mathematics Subject Classification: 18F, 18E40, 16G, 16D90, 16E

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

View Paper: https://www.semanticscholar.org/paper/97a82a8fe0a6d9ddabc0b6fcbc630655f7ac3257

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Gorenstein Homological Aspects of Monomorphism Categories via Morita Rings (2015, background): “4] and for more details on recollements of abelian categories we refer to [23, 36].”
On Artin Algebras Arising from Morita Contexts (2013, background): “For the notion of recollements of abelian categories we refer to [18], [33].”
Realisation functors in tilting theory (2015, background): “Recollements of both abelian and triangulated categories appeared in [16], but the properties of recollements of abelian categories were only explored later, for example in [32].”
Gorenstein categories, singular equivalences and finite generation of cohomology rings in recollements (2014, background): “Our purpose in this section is to study singularity categories, in the sense of Buchweitz [12] and Orlov [50], in a recollement of abelian categories (A ,B,C ).”