nLab virtual equipment

Contents

Contents

Idea

A proarrow equipment on a virtual double category or virtual equipment for short is a virtual double category equipped with the same kind of structure that makes an ordinary double category into a proarrow equipment.

Virtual equipments are the structures that support structures of generalized multicategories.

Definition

Definition

A virtual equipment is a virtual double category in which all units and all restrictions exist.

This is (CruttwellShulman, def. 7.6).

References

The formal category theory of monads and adjunctions (and more generally relative monads and relative adjunctions) is developed in:

On a string diagram-calculus for (virtual) double categories with (virtual) pro-arrow equipments:

A type system with semantics in virtual equipments:

  • Max S. New and Daniel R. Licata. 2023. A Formal Logic for Formal Category Theory. In Foundations of Software Science and Computation Structures - 26th International Conference, FoSSaCS 2023. DOI

Last revised on September 20, 2024 at 18:08:53. See the history of this page for a list of all contributions to it.