Internal lenses as functors and cofunctors
From MaRDI portal
Publication:6349106
arXiv2009.06835MaRDI QIDQ6349106
Publication date: 14 September 2020
Abstract: Lenses may be characterised as objects in the category of algebras over a monad, however they are often understood instead as morphisms, which propagate updates between systems. Working internally to a category with pullbacks, we define lenses as simultaneously functors and cofunctors between categories. We show that lenses may be canonically represented as a particular commuting triangle of functors, and unify the classical state-based lenses with both c-lenses and d-lenses in this framework. This new treatment of lenses leads to considerable simplifications that are important in applications, including a clear interpretation of lens composition.
Special properties of functors (faithful, full, etc.) (18A22) Closed categories (closed monoidal and Cartesian closed categories, etc.) (18D15)
This page was built for publication: Internal lenses as functors and cofunctors
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6349106)
