https://github.com/mattecapu/awesome-double-categories

A list of works and resources about double category theory, with a particular focus on applications.
https://github.com/mattecapu/awesome-double-categories

List: awesome-double-categories

applied-category-theory category-theory double-categories mathematics

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A list of works and resources about double category theory, with a particular focus on applications.

• Host: GitHub
• URL: https://github.com/mattecapu/awesome-double-categories
• Owner: mattecapu
• Created: 2022-10-16T00:29:26.000Z (about 2 years ago)
• Default Branch: master
• Last Pushed: 2022-10-19T14:54:50.000Z (about 2 years ago)
• Last Synced: 2024-05-22T21:00:38.155Z (6 months ago)
• Topics: applied-category-theory, category-theory, double-categories, mathematics
• Homepage:
• Size: 2.93 KB
• Stars: 24
• Watchers: 3
• Forks: 2
• Open Issues: 2
• Metadata Files:
  • Readme: README.md

Awesome Lists containing this project

README

        
# Awesome Double Categories

A list of works and resources about double category theory, with a particular focus on applications.

(If you'd like to add more, edit [this nLab page](https://ncatlab.org/nlab/show/applications+of+double+category+theory))

## Introductions & references

* The Catsters, [_Double categories_](https://www.youtube.com/watch?v=kiCZiSA2W3Q) (short video)

* Grandis, [_Higher dimensional categories: from double to multiple categories_](https://doi.org/10.1142/11406), 2019,

* Johnson, Yau, [_2-Dimensional Categories_](http://arxiv.org/abs/2002.06055) (Section 12.3), 2020

* nLab, [_double category_](https://ncatlab.org/nlab/show/double+category)

## Theory

### General

* Grandis, Parè, [_Limits in double categories_](http://www.numdam.org/article/CTGDC_1999__40_3_162_0.pdf), 1999

* Grandis, Parè, [_Adjoints for double categories_](http://www.numdam.org/article/CTGDC_2004__45_3_193_0.pdf),2004

* Myers, [_String diagrams for double categories and (virtual) equipments_](https://arxiv.org/abs/1612.02762), 2016

### Equipments

* Shulman, [_Equipments_](https://golem.ph.utexas.edu/category/2009/11/equipments.html), 2009

* Shulman, [_Framed bicategories and monoidal fibrations_](https://arxiv.org/abs/0706.1286), 2009

### Grothendieck constructions

* Patterson, [_Grothendieck construction for double categories_](https://topos.site/blog/2022/05/grothendieck-construction-for-double-categories/), 2022

* Cruttwell, Lambert, Pronk, Szyld, [_Double Fibrations_](https://arxiv.org/abs/2205.15240), 2022

## Applications

### Lenses & optics

* Clarke, [_The double category of lenses_](https://bryceclarke.github.io/The_Double_Category_Of_Lenses_Phd_Thesis.pdf), 2022

* Capucci, [_Seeing double through dependent optics_](https://arxiv.org/abs/2204.10708), 2022

### Open systems theory

* Courser, [_Open systems: a double categorical perspective_](https://arxiv.org/abs/2008.02394), 2020

* Patterson, [_Decorated cospans via the double Grothendieck construction_](https://topos.site/blog/2022/05/decorated-cospans-via-the-grothendieck-construction/), 2022

* Baez, Courser, Vasilakopoulou, [_Structured versus Decorated Cospans_](https://compositionality-journal.org/papers/compositionality-4-3/pdf), 2022

* Myers, [_Categorical systems theory_](http://davidjaz.com/Papers/DynamicalBook.pdf), 2021