  We give a specific cylinder functor for semifree dg categories. This allows
us to construct a homotopy colimit functor explicitly. These two functors are
"computable", specifically, the constructed cylinder functor sends a dg
category of finite type, i.e., a semifree dg category having finitely many
generating morphisms, to a dg category of finite type. The homotopy colimit
functor has a similar property. Moreover, using the cylinder functor, we give a
cofibration category of semifree dg categories and that of dg categories of
finite type, independently from the work of Tabuada. All the results similarly
work for semifree dg algebras. We also describe an application to symplectic
topology and provide a toy example.
