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)

Introductions & references

• The Catsters, Double categories (short video)
• Grandis, Higher dimensional categories: from double to multiple categories, 2019,
• Johnson, Yau, 2-Dimensional Categories (Section 12.3), 2020
• nLab, double category

Theory

General

• Grandis, Parè, Limits in double categories, 1999
• Grandis, Parè, Adjoints for double categories,2004
• Myers, String diagrams for double categories and (virtual) equipments, 2016

Equipments

• Shulman, Equipments, 2009
• Shulman, Framed bicategories and monoidal fibrations, 2009

Grothendieck constructions

• Patterson, Grothendieck construction for double categories, 2022
• Cruttwell, Lambert, Pronk, Szyld, Double Fibrations, 2022

Applications

Lenses & optics

• Clarke, The double category of lenses, 2022
• Capucci, Seeing double through dependent optics, 2022

Open systems theory

• Courser, Open systems: a double categorical perspective, 2020
• Patterson, Decorated cospans via the double Grothendieck construction, 2022
• Baez, Courser, Vasilakopoulou, Structured versus Decorated Cospans, 2022
• Myers, Categorical systems theory, 2021