  We construct a new cylinder object for semifree differential graded (dg)
categories in the category of dg categories. Using this, we give a practical
formula computing homotopy colimits of semifree dg categories. Combining it
with the result of Ganatra, Pardon, and Shende, we get a formula computing
wrapped Fukaya categories of Weinstein manifolds using their sectorial
coverings. This formula has lots of applications including a practical
computation of the wrapped Fukaya category of any cotangent bundle or plumbing
space. In this paper, we compute wrapped Fukaya categories of cotangent bundles
of lens spaces using their Heegaard decomposition. From the computation, we
show that the endomorphism algebra of the cotangent fibre is a full invariant
of the homotopy type of lens spaces.
