Work

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

Year: 2024

Type: article

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. 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

Source: Electronic Notes in Theoretical Informatics and Computer Science

DOI: 10.46298/entics.14638

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

Institutions: Florida State University, Oak Ridge National Laboratory, University of Strathclyde, Chapman University

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid