  Consider the partition function of a classical system in two spatial
dimensions, or the Euclidean path integral of a quantum system in two
space-time dimensions, both on a lattice. We show that the tensor network
renormalization (TNR) algorithm [\emph{G. Evenbly and G. Vidal, Phys. Rev.
Lett. 115, 180405}] can be used to implement local scale transformations on
these objects, namely a lattice version of conformal maps. Specifically, we
explain how to implement the lattice equivalent of the logarithmic conformal
map that transforms the Euclidean plane into a cylinder. As an application, and
with the 2D critical Ising model as a concrete example, we use this map to
build a lattice version of the scaling operators of the underlying conformal
field theory, from which one can extract their scaling dimensions and operator
product expansion coefficients.
