# Generalized Lens Categories via functors Crm op→mathsfCat

arXiv: https://arxiv.org/abs/1908.02202 · HTML: https://mlsanity.com/paper/1908.02202/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Aug 2019.

## Built on by (most cited first, 1 of 1)

- [Deep Learning with Parametric Lenses](https://mlsanity.com/paper/2404.00408/) (2024)

## Abstract (arXiv)

Lenses have a rich history and have recently received a great deal of attention from applied category theorists. We generalize the notion of lens by defining a category mathsfLensF for any category C and functor Fcolon Crm op→mathsfCat, using a variant of the Grothendieck construction. All of the mathematics in this note is straightforward; the purpose is simply to see lenses in a broader context where some closely-related examples, such as ringed spaces and open continuous dynamical systems, can be included.