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Categorical matrix factorizations

Petter Andreas Bergh and David A. Jorgensen
Vol. 8 (2023), No. 3, 355–378
DOI: 10.2140/akt.2023.8.355
Abstract

We give a purely categorical construction of d-fold matrix factorizations of a natural transformation, for any even integer d. This recovers the classical definition of those for regular elements in commutative rings due to Eisenbud. We explore some natural functors between associated triangulated categories, and show that when d = 2 these are full and faithful, and in some cases equivalences.

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Keywords
matrix factorizations, triangulated categories
Mathematical Subject Classification
Primary: 13D02, 18E05, 18G35, 18G80
Milestones
Received: 10 July 2022
Revised: 5 June 2023
Accepted: 4 July 2023
Published: 27 August 2023
Authors
Petter Andreas Bergh
Department of Mathematical Sciences
NTNU
Institutt for Matematiske Fag
Trondheim
Norway
David A. Jorgensen
Department of Mathematics
University of Texas at Arlington
Arlington, TX
United States
© 2023 MSP (Mathematical Sciences Publishers).