arXiv
Open Access
2024
On a fibrational construction for optics, lenses, and Dialectica categories
Matteo Capucci
Bruno Gavranović
Abdullah Malik
Francisco Rios
Jonathan Weinberger
Abstrak
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.
Penulis (5)
M
Matteo Capucci
B
Bruno Gavranović
A
Abdullah Malik
F
Francisco Rios
J
Jonathan Weinberger
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