On a fibrational construction for optics, lenses, and Dialectica categories
<|reference_start|>On a fibrational construction for optics, lenses, and Dialectica categories: Categories of lenses/optics and Dialectica categories are both comprised of bidirectional morphisms of basically the same form. In this work we show how they can be considered a special case of an overarching fibrational construction, generalizing Hofstra's construction of Dialectica fibrations and Spivak's construction of generalized lenses. This construction turns a tower of Grothendieck fibrations into another tower of fibrations by iteratively twisting each of the components, using the opposite fibration construction.<|reference_end|>
@article{capucci2024on,
    title={On a fibrational construction for optics, lenses, and Dialectica
  categories},
    author={Matteo Capucci, Bruno Gavranovi'c, Abdullah Malik, Francisco Rios,
  Jonathan Weinberger},
    journal={arXiv preprint arXiv:2403.16388},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.16388},
    primaryClass={math.CT cs.IT cs.LO math.IT}
}