Enriched lenses

Bryce Clarke – 27 October 2021

In this talk, I will provide an introduction to lenses between enriched categories, generalising the ordinary case of (delta) lenses between locally small categories. Just as in the ordinary case, enriched lenses will consist of a compatible enriched functor and enriched cofunctor, the latter which will be defined using retrocells (due to Robert Paré) in the double category of matrices V-Mat for a distributive monoidal category V. The talk will conclude with some examples, including weighted lenses (for V = wSet, the monoidal category of weighted sets) which were introduced in the recent paper by Paolo Perrone (arXiv:2110.06591).