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Lenses have a rich history and have recently received a great deal ofattention from applied category theorists. We generalize the notion of lens bydefining a category $\mathsf{Lens}_F$ for any category $\mathcal{C}$ andfunctor $F\colon \mathcal{C}^{\rm op}\to\mathsf{Cat}$, using a variant of theGrothendieck construction. All of the mathematics in this note isstraightforward; the purpose is simply to see lenses in a broader context wheresome closely-related examples, such as ringed spaces and open continuousdynamical systems, can be included.

Generalized Lens Categories via functors $\mathcal{C}^{\rm op}\to\mathsf{Cat}$