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.

翻译：透镜/光学范畴与辩证范畴均由形式基本相同的双向态射构成。本文论证了它们如何可被视为一个总体纤维化构造的特例，该构造推广了霍夫斯特拉的辩证纤维化构造与斯皮瓦克的广义透镜构造。通过运用对偶纤维化构造对每个分量进行迭代扭转，该构造将格罗滕迪克纤维化塔转化为另一个纤维化塔。