  Lenses are an important tool in applied category theory. While individual
lenses have been widely used in applications, many of the mathematical
properties of the corresponding categories of lenses have remained unknown. In
this paper, we study the category of small categories and asymmetric delta
lenses, and prove that it has several good exactness properties. These
properties include the existence of certain limits and colimits, as well as
so-called imported limits, such as imported products and imported pullbacks,
which have arisen previously in applications. The category is also shown to be
extensive, and it has an image factorisation system.
