Morita Theory For Derived Categories: A Bicategorical Perspective
Algebraic Topology
2008-06-03 v2 Category Theory
Rings and Algebras
Abstract
We present a bicategorical perspective on derived Morita theory for rings, DG algebras, and spectra. This perspective draws a connection between Morita theory and the bicategorical Yoneda Lemma, yielding a conceptual unification of Morita theory in derived and bicategorical contexts. This is motivated by study of Rickard's theorem for derived equivalences of rings and of Morita theory for ring spectra, which we present in Sections 2 and 4. Along the way, we gain an understanding of the barriers to Morita theory for DG algebras and give a conceptual explanation for the counterexample of Dugger and Shipley.
Keywords
Cite
@article{arxiv.0805.3673,
title = {Morita Theory For Derived Categories: A Bicategorical Perspective},
author = {Niles Johnson},
journal= {arXiv preprint arXiv:0805.3673},
year = {2008}
}
Comments
20 pages; minor update to introduction; contact information added