Definitions
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Structures on 2-categories
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.
A virtual equipment is a virtual double category in which all units and all restrictions exist.
This is (CruttwellShulman, def. 7.6).
The formal category theory of monads and adjunctions (and more generally relative monads and relative adjunctions) is developed in:
Nathanael Arkor, Dylan McDermott, The formal theory of relative monads, Journal of Pure and Applied Algebra 107676. (2024) [arXiv:2302.14014]
Nathanael Arkor, Dylan McDermott, Relative monadicity (2023) [arXiv:2305.10405]
Nathanael Arkor, Dylan McDermott, The pullback theorem for relative monads (2024) [arXiv:2404.01281]
On a string diagram-calculus for (virtual) double categories with (virtual) pro-arrow equipments:
David Jaz Myers, String Diagrams For Double Categories and (Virtual) Equipments [arXiv:1612.02762]
David Jaz Myers, String Diagrams for (Virtual) Proarrow Equipments (2017) [slides: pdf, pdf]
A type system with semantics in virtual equipments:
Last revised on September 20, 2024 at 18:08:53. See the history of this page for a list of all contributions to it.