Generalized Lens Categories via Functors from Cop to Cat

paper

Generalized Lens Categories via functors ${\mathcal{C}}^{\mathrm{op}}\to \mathsf{Cat}$ — David I. Spivak (2019). arXiv:1908.02202 (v4, PDF).

Observes that the Grothendieck construction of the fibrewise opposite of an indexed category ${\mathcal{C}}^{\mathrm{op}}\to \mathbf{Cat}$ yields a category of generalised lenses, recovering ordinary lenses from the simple fibration and giving a uniform source of bidirectional morphisms (including those of polynomial functors).

Sources: the paper, arXiv:1908.02202v4, checked against the arXiv listing. Index: Papers.

Key definitions and results

• Grothendieck lenses $\int F^{\mathrm{op}}$

Concept notes

Grothendieck Construction, Lens, Bayesian Lens