Mathematics – Category Theory
Scientific paper
2009-05-17
Memoirs of the Amer. Math. Soc. 212 (2011), no.996, v+133 pp
Mathematics
Category Theory
LaTeX 2e, 144 pages. v.4: Examples added in subsection 9.4, other small additions, many misprints corrected; v.5: New subsecti
Scientific paper
10.1090/S0065-9266-2010-00631-8
This paper can be thought of as an extended introduction to arXiv:0708.3398; nevertheless, most of its results are not covered by loc. cit. We consider the derived categories of DG-modules, DG-comodules, and DG-contramodules, the coderived and contraderived categories of CDG-modules, the coderived categories of CDG-comodules, and the contraderived categories of CDG-contramodules. The equivalence between the latter two categories (the comodule-contramodule correspondence) is established. Nonhomogeneous Koszul duality or "triality" (an equivalence between exotic derived categories corresponding to Koszul dual (C)DG-algebra and CDG-coalgebra) is obtained in the conilpotent and nonconilpotent versions. Various A_\infty-structures are considered, and a number of model category structures are described. Homogeneous Koszul duality and D-\Omega duality are discussed in the appendices.
No associations
LandOfFree
Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-514070