  We develop the basic theory of smooth representations of locally compact
groups on bornological vector spaces. In this setup, we are able to formulate
better general theorems than in the topological case. Still, smooth
representations of totally disconnected groups on vector spaces and of Lie
groups on Frechet spaces remain special cases of our theory. We identify smooth
representations with essential modules over an appropriate convolution algebra.
We examine smoothening functors on representations and modules and show that
they agree if they are both defined. We establish the basic properties of
induction and compact induction functors using adjoint functor techniques. We
describe the center of the category of smooth representations.
