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ENHANCED FINITE TRIANGULATED CATEGORIES

Part of: Operations and obstructions Abelian categories Homological algebra Homological methods

Published online by Cambridge University Press:  18 June 2020

Fernando Muro Open the ORCID record for Fernando Muro [Opens in a new window]
Fernando Muro*
Affiliation:
Universidad de Sevilla, Facultad de Matemáticas, Departamento de Álgebra, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain (fmuro@us.es) URL: https://personal.us.es/fmuro
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Abstract

We give a necessary and sufficient condition for the existence of an enhancement of a finite triangulated category. Moreover, we show that enhancements are unique when they exist, up to Morita equivalence.

Keywords

Triangulated categoryA-infinity categoryHochschild cohomologyspectral sequenceobstruction theory

MSC classification

Primary: 18E30: Derived categories, triangulated categories
Secondary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 18G40: Spectral sequences, hypercohomology 55S35: Obstruction theory
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 3 , May 2022 , pp. 741 - 783
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Copyright
© The Author(s) 2020. Published by Cambridge University Press

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