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arXiv · 2209.01144

An introduction to enriched cofunctors

Bryce Clarke·Matthew Di Meglio
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Abstract

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.

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Bryce Clarke, Matthew Di Meglio. 2022-09-02. An introduction to enriched cofunctors. https://arxiv.org/abs/2209.01144

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