  We show that the blocks of category O for the Lie superalgebra q_n associated
to half-integral weights carry the structure of a tensor product
categorification for the infinite rank Kac-Moody algebra of type C. This allows
us to prove two conjectures formulated by Cheng, Kwon and Lam. We then focus on
the full subcategory consisting of finite-dimensional representations, which we
show is a highest weight category with blocks that are Morita equivalent to
certain generalized Khovanov arc algebras.
