  In this paper, we apply the idea of T-duality to projective spaces. From a
connection on a line bundle on $\mathbb P^n$, a Lagrangian in the mirror
Landau-Ginzburg model is constructed. Under this correspondence, the full
strong exceptional collection $\mathcal O_{\mathbb P^n}(-n-1),...,\mathcal
O_{\mathbb P^n}(-1)$ is mapped to standard Lagrangians in the sense of
\cite{nz}. Passing to constructible sheaves, we explicitly compute the quiver
structure of these Lagrangians, and find that they match the quiver structure
of this exceptional collection of $\mathbb P^n$. In this way, T-duality
provides quasi-equivalence of the Fukaya category generated by these
Lagrangians and the category of coherent sheaves on $\mathbb P^n$, which is a
kind of homological mirror symmetry.
