Bryce Clarke (Partout team, INRIA), Reflections on delta lenses



What is a lens? As with many questions in mathematics, the answer depends on who you ask! Delta lenses are a particular kind of lens introduced in 2011 to model bidirectional transformations between systems. In elementary terms, a delta lens is a functor equipped with a suitable choice of lifts, generalising the notion of split opfibration. However, despite admitting a simple definition, many of the interesting and natural category-theoretic properties of delta lenses remain hidden from view without alternative characterisations. In this talk, I will reflect upon several perspectives of delta lenses developed in my PhD thesis, The double category of lenses, and demonstrate their richness as a mathematical structure. The talk will explore the connections between these different approaches, while emphasising the relationship between lenses and double categories, and conclude with several avenues for future work.