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Aarhus Universitets segl

The Q-shaped derived category of a ring

Henrik Holm (University of Copenhagen)
Onsdag 1. december 2021 14:15–15:00 G3.1 (1532-314)
Mathematics seminar

The derived category D(A) of the category Mod(A) of modules over a ring A is an important example of a triangulated category in algebra. It can be obtained as the homotopy category of the category Ch(A) of chain complexes of A-modules equipped with its standard model structure. One can view Ch(A) as the category Fun(Q,Mod(A)) of additive functors from a special (but quite natural) small preadditive category Q to Mod(A). Note that the model structure on Ch(A) = Fun(Q,Mod(A)) is not inherited from a model structure on Mod(A) but arises instead from the "self-injectivity" of the special category Q. We will show that the functor category Fun(Q,Mod(A)) has two interesting model structures for many other self-injective small preadditive categories Q. These two model structures have the same weak equivalences, and the associated homotopy category is what we call the Q-shaped derived category of A. We will also show that it is possible to generalize the homology functors on Ch(A) to homology functors on Fun(Q,Mod(A)) for most self-injective small preadditive categories Q. The talk is based on a joint paper with Peter Jørgensen (arXiv:2101.06176), which has the same title as the talk.

Organiseret af: AarHomAlg
Kontakt: Peter Jørgensen Revideret: 25.05.2023