Название: The contra version of the category O
Аннотация: The semicoderived category of the category O over the Virasoro or Kac-Moody Lie algebra is equivalent to the semicontraderived category of the contra version of the category O with the complementary or shifted central charge. In this paper we show that the forgetful functor from the contra version of the category O into the category of modules over the Lie algebra is fully faithful. Similarly, the forgetful functor from the category of contramodules over the topological Lie algebra into the category of modules over the underlying discrete Lie algebra is fully faithful for Lie algebras such as the Virasoro and Kac-Moody. These assertions extend the line of known results claiming that the forgetful functors from contramodules to modules are fully faithful under certain assumptions.