Let be a differential graded category.
A twisted complex in is
a graded set of objects of , such that only finitely many are not the zero object;
a set of morphisms such that
The differential graded category of twisted complexes in has as objects twisted complexes and
with differential given on given by
The construction of categories of twisted complexes is functorial in that for a dg-functor, there is a dg-functor
Passing from a dg-category to its category of twisted complexes is a step towards enhancing it to a pretriangulated dg-category.
- Landau-Ginzburg model, pretriangulated dg-category
- Alexei Bondal, Mikhail Kapranov, Enhanced triangulated categories, Матем. Сборник, Том 181 (1990), No.5, 669–683 (Russian); transl. in USSR Math. USSR Sbornik, vol. 70 (1991), No. 1, pp. 93–107, (MR91g:18010) (Bondal-Kapranov Enhanced triangulated categories pdf)
- Bernhard Keller, A brief introduction to -algebras (pdf)
- Mikhail Kapranov, Svyatoslav Pimenov, Derived varieties of complexes and Kostant’s theorem for gl(m|n), arxiv/1504.00339
Revised on April 2, 2015 14:11:37
by Zoran Škoda