  We study concrete sheaf models for a call-by-value higher-order language with
recursion. Our family of sheaf models is a generalization of many examples from
the literature, such as models for probabilistic and differentiable
programming, and fully abstract logical relations models. We treat recursion in
the spirit of synthetic domain theory. We provide a general construction of a
lifting monad starting from a class of admissible monomorphisms in the site of
the sheaf category. In this way, we obtain a family of models parametrized by a
concrete site and a class of monomorphisms, for which we prove a general
computational adequacy theorem.
