Abstract
Differential graded (dg) categories provide enhancements of triangulated categories that allow us to overcome some problems that come from working solely with the triangulated structure. In this talk, we present the definition of dg categories and describe some constructions that can be performed with them. We then consider how a dg category provides an enhancement of a triangulated category, and show how to compute some important invariants of the category using such a dg enhancement. Finally we’ll present some theorems about such invariants, and how to derive them using properties of the dg enhancement. This talk is purely expository and does not contain original material; it is mostly based on B. Keller’s excellent survey on dg categories [9], and whenever possible I have used notation compatible with that source. I also included material and examples from the other sources listed as references as well.
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Takeda, A.A. (2018). Introduction to Differential Graded Categories. In: Ballard, M., Doran, C., Favero, D., Sharpe, E. (eds) Superschool on Derived Categories and D-branes. SDCD 2016. Springer Proceedings in Mathematics & Statistics, vol 240. Springer, Cham. https://doi.org/10.1007/978-3-319-91626-2_10
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DOI: https://doi.org/10.1007/978-3-319-91626-2_10
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