  A comprehensive account of the categorical properties of the category of
small categories and asymmetric delta lenses is given in the recent works of
Chollet et al. and Di Meglio. An important construction for proving many of
these properties is Johnson and Rosebrugh's "pullback" of lenses, which we call
the proxy pullback of lenses. We give a new treatment of the proxy pullback in
terms of compatibility, a stronger notion of commutativity for squares of
lenses. The proxy pullback is sometimes, but not always, a real pullback. Using
new notions of sync-minimal and independent lens spans, we characterise when a
lens span that forms a commuting square with a lens cospan has a comparison
lens to a proxy pullback of the cospan.
