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Mathematics, Category Theory, Computer Science, Information Theory
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.
