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

Abstract

Lenses have a rich history and have recently received a great deal of attention from applied category theorists. We generalize the notion of lens by defining a category ${\mathsf{Lens}}_F$ for any category $\mathcal{C}$ and functor $F:{\mathcal{C}}^{\mathrm{op}}\to \mathsf{Cat}$, using a variant of the Grothendieck construction. All of the mathematics in this note is straightforward; the purpose is simply to see lenses in a broader context where some closely-related examples, such as ringed spaces and open continuous dynamical systems, can be included.

10 pages. (This version: fix some typos)

References in corpus (4)

• Monoidal Grothendieck construction
• Coherence for lenses and open games
• Categories of Optics
• On the Existence of an Orthogonal Factorization System on 1-Cob and 2-Cob

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