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Conference Paper

On a fibrational construction for optics, lenses, and Dialectica categories

MPS-Authors
/persons/resource/persons297260

Weinberger,  Jonathan       
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.48550/arXiv.2403.16388
(Preprint)

https://doi.org/10.46298/entics.proceedings.mfps40
(Publisher version)

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Fulltext (public)

2403.16388.pdf
(Preprint), 261KB

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Citation

Capucci, M., Gavranović, B., Malik, A., Rios, F., & Weinberger, J. (2024). On a fibrational construction for optics, lenses, and Dialectica categories. In Electronic Notes in Theoretical Informatics and Computer Science: Proceedings of MFPS XL. EPI sciences.


Cite as: https://hdl.handle.net/21.11116/0000-0010-5829-E
Abstract
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.