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Lenses are an important tool in applied category theory. While individuallenses have been widely used in applications, many of the mathematicalproperties of the corresponding categories of lenses have remained unknown. Inthis paper, we study the category of small categories and asymmetric deltalenses, and prove that it has several good exactness properties. Theseproperties include the existence of certain limits and colimits, as well asso-called imported limits, such as imported products and imported pullbacks,which have arisen previously in applications. The category is also shown to beextensive, and it has an image factorisation system.

Limits and Colimits in a Category of Lenses