The Tilting–Cotilting Correspondence
By L. Positselski, J. Št’ovíček. International mathematics research notices, 2017
47 citations recorded by the source corpus.
To a big $n$-tilting object in a complete, cocomplete abelian category ${\textsf{A}}$ with an injective cogenerator we assign a big $n$-cotilting object in a complete, cocomplete abelian category ${\textsf{B}}$ with a projective generator and vice versa. Then we construct an equivalence between the (conventional or absolute) derived categories of ${\textsf{A}}$ and ${\textsf{B}}$. Under various assumptions on ${\textsf{A}}$, which cover a wide range of examples (for instance, if ${\textsf{A}}$ is a module category or, more generally, a locally finitely presentable Grothendieck abelian category), we show that ${\textsf{B}}$ is the abelian category of contramodules over a topological ring and that the derived equivalences are realized by a contramodule-valued variant of the usual derived Hom functor.
View Paper: https://www.semanticscholar.org/paper/c95bbe0027f7cc2af207f9837dbb5797989d68be
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- J. Št’ovíček
- Lidia Angeleri Hugel
- L. Positselski
- Chrysostomos Psaroudakis
- Pedro Nicolás
- James Gillespie
- Manuel Saor'in
Citations in the corpus
- ∞-tilting theory (2017, background): “n homological algebra in (2), to the representation theory of infinite-dimensional Lie algebras (e.g. the Virasoro or Kac–Moody algebras) in (3). A part of the work has been done in our previous paper [49], where we explained how the finite generation assumption can be naturally dropped with help of a”