The 2-Adjunction that relates Universal Arrows and Extensive Monads

TL;DR

This paper constructs an explicit 2-adjunction linking universal arrows and extensive monads, providing foundational insights that could impact theories of pseudo adjunctions and practical applications in computer science.

Contribution

It explicitly constructs a 2-adjunction connecting universal arrows and extensive monads, revealing structural isomorphisms in 2-category theory.

Findings

2-adjunction explicitly constructed

Isomorphism between 2-categories of universal arrows and adjunctions

Potential applications in pseudo adjunctions and computer science

Abstract

In this article the 2-adjunction that relates universal arrows and extensive monads is constructed explicitly. This 2-adjunction resembles the one that relates adjunctions and monads since the 2-category of universal arrows is isomorphic to the 2-category of adjunctions and the 2-category of extensive monads is isomorphic to the 2-category of monads. This article would be useful as a foundation for a theory relating pseudo adjunctions and pseudo monads for Gray-categories. On the other hand, it might function as an accesible tool for computer scientists on extensive monads.