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The 2-Adjunction that relates Universal Arrows and Extensive Monads
Adrian Vazquez-Marquez, Jenylin Zuniga-Apipilhuasco · 2025-02-25 · via cs.IT updates on arXiv.org

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.

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