# Multicategories of Multiary Lenses

@inproceedings{Johnson2019MulticategoriesOM, title={Multicategories of Multiary Lenses}, author={Michael Johnson and Robert D. Rosebrugh}, booktitle={Bx@PLW}, year={2019} }

Recently lens-like definitions of multidirectional transformations have appeared [2], encompassing both a “propagation” form (in the style of [5]) and a “wide span” form (in the style of [6]). These “multiary lenses” raise a number of new challenges that are addressed in this paper. First, in common with classical symmetric lenses, they need to be studied modulo equivalence relations that factor out differences in hidden data and declare two lenses to be equivalent if their observable…

## 4 Citations

### Lenses and Learners

- MathematicsBx@PLW
- 2019

This paper shows both that there is a faithful, identity-on-objects symmetric monoidal functor embedding a category of asymmetric lenses into the category of learners, and furthermore there is such a functorEmbedding the categories of learners into a categories of symmetric lenses.

### Controllable and decomposable multidirectional synchronizations

- Computer ScienceSoftw. Syst. Model.
- 2021

Very well-behaved multidirectional transformations are characterized, a non-trivial generalization from the bidirectional case, and a novel concept of controllability is introduced for the former challenge, while for the latter one a novel formal notion of faithful decomposition is proposed.

### The more legs the merrier: A new composition for symmetric (multi-)lenses

- Business
- 2021

This paper develops a new composition of symmetric lenses that preserves information which is important for implementing system interoperation. It includes a cut-down but realistic example of a…

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