@inproceedings{2071cd9580194e7fad76e0ce11cf730d,
title = "A Brief Introduction to the Q-Shaped Derived Category",
abstract = "A chain complex can be viewed as a representation of a certain quiver with relations, Qcpx. The vertices are the integers, there is an arrow q right arrow Overscript Endscripts q minus 1) for each integer q, and the relations are that consecutive arrows compose to 0. Hence the classic derived category D can be viewed as a category of representations of Qcpx. It is an insight of Iyama and Minamoto that the reason D is well behaved is that, viewed as a small category, Qcpx has a Serre functor. Generalising the construction of D to other quivers with relations which have a Serre functor results in the Q-shaped derived category, DQ. Drawing on methods of Hovey and Gillespie, we developed the theory of DQ in three recent papers. This paper offers a brief introduction to DQ, aimed at the reader already familiar with the classic derived category.",
keywords = "Abelian category, Abelian model category, Chain complex, Cofibration, Derived category, Exact category, Fibration, Frobenius category, Homotopy, Homotopy category, Model category, Stable category, Triangulated category, Weak equivalence",
author = "Henrik Holm and Peter J{\o}rgensen",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; Abel Symposium, 2022 ; Conference date: 06-06-2022 Through 10-06-2022",
year = "2024",
doi = "10.1007/978-3-031-57789-5\_5",
language = "English",
isbn = "9783031577888",
series = "Abel Symposia",
publisher = "Springer",
pages = "141--167",
editor = "Bergh, \{Petter Andreas\} and {\O}yvind Solberg and Steffen Oppermann",
booktitle = "Triangulated Categories in Representation Theory and Beyond",
address = "Netherlands",
}