On a fibrational construction for optics, lenses, and Dialectica categories
- Resource Type
- Working Paper
- Authors
- Capucci, Matteo; Gavranović, Bruno; Malik, Abdullah; Rios, Francisco; Weinberger, Jonathan
- Source
- Subject
- Mathematics - Category Theory
Computer Science - Information Theory
Computer Science - Logic in Computer Science
18M35, 18D30, 18M05, 03G30, 03B38
F.4.1
- Language
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: v2: 18 pp. Project results from the American Mathematical Society's Math Research Community on Applied Category Theory 2022. Some corrections and clarifications after peer review. Accepted pre-proceedings version for MFPS 2024