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. 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
Authors
- Jonathan Weinberger
- Matteo Capucci
- Bruno Gavranović (ORCID: https://orcid.org/0000-0002-6069-5727)
- Abdullah Malik
- Francisco Rios
Institutions
- Florida State University (US)
- Oak Ridge National Laboratory (US)
- University of Strathclyde (GB)
- Chapman University (US)
- Quantum Science Center (US)
Publication Details
- Journal
- Electronic Notes in Theoretical Informatics and Computer Science
- Published
- 2024-12-11
- DOI
- https://doi.org/10.46298/entics.14638
- Primary Topic
- Homotopy and Cohomology in Algebraic Topology
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Johns Hopkins University
- Multidisciplinary University Research Initiative
- Medical Research Council
- Army Research Office