Universal Properties of Lens Proxy Pullbacks

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