Matteo Capucci ; Bruno Gavranović ; Abdullah Malik ; Francisco Rios ; Jonathan Weinberger - On a fibrational construction for optics, lenses, and Dialectica categories

entics:14638 - Electronic Notes in Theoretical Informatics and Computer Science, December 11, 2024, Volume 4 - Proceedings of MFPS XL - https://doi.org/10.46298/entics.14638
On a fibrational construction for optics, lenses, and Dialectica categoriesArticle

Authors: Matteo Capucci ; Bruno Gavranović ; Abdullah Malik ; Francisco Rios ; Jonathan Weinberger

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.

Comment: v3: 18 pp. Project results from the American Mathematical Society's Math Research Community on Applied Category Theory 2022. v4: Final version for proceedings of MFPS 2024. Updated author affiliation. v5: Corrected author typo, added MPIM report no and DOI

https://doi.org/10.46298/entics.14638
Source: arXiv.org:2403.16388
Volume: Volume 4 - Proceedings of MFPS XL
Published on: December 11, 2024
Accepted on: November 7, 2024
Submitted on: June 3, 2024
Keywords: Mathematics - Category Theory, Computer Science - Information Theory, Computer Science - Logic in Computer Science, 18M35, 18D30, 18M05, 03G30, 03B38, F.4.1
Licence: Attribution 4.0 International (CC BY 4.0)
Funding:
    Source : OpenAIRE Graph
  • Mathematics Research Communities; Funder: National Science Foundation; Code: 1916439

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