2024/03/25 by Matteo Capucci, Bruno Gavranović, Abdullah Malik +2 · 1 voice
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #Algebraic structures and combinatorial models
paper · pdf · doi:10.46298/entics.14638
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