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.

A long theory paper on actions of monoidal categories and their properties. We describe distributive laws between monoidal and actegorical structures and provide examples of their use in the theory of optics and parametric morphisms.

Twitter thread.

An outline of some ideas we had lately on the problem of dependent optics, including some solutions.

Twitter thread.

An invitation to some new and old mathematical gadgets and their use to model cybernetic systems, including but not limited to open games and machine learning.