2022/09/02 by Bryce Clarke, Clarke, Bryce, Matthew Di Meglio +1
Mathematics · #18D20 #18N10 #Adjoint functors #Artificial intelligence #Category Theory (math.CT) #Computer science #Data mining #Distributive property #Enriched category #FOS: Mathematics #Functor #Homotopy and Cohomology in Algebraic Topology #Lift (data mining) #Mathematics #Monoidal category #Morphism #Natural transformation #Object (grammar) #Pure mathematics
paper · pdf · doi:10.48550/arxiv.2209.01144
openalex publication_date 2022/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Cofunctors are a kind of map between categories which lift morphisms along an object assignment. In this paper, we introduce cofunctors between categories enriched in a distributive monoidal category. We define a double category of enriched categories, enriched functors, and enriched cofunctors, whose horizontal and vertical 2-categories have 2-cells given by enriched natural transformations between functors and cofunctors, respectively. Enriched lenses are defined as a compatible enriched functor and enriched cofunctor pair; weighted lenses, which were introduced by Perrone, are precisely lenses enriched in weighted sets. Several other examples are also studied in detail.