ABSTRACT
We construct a $3$-categorical presentation $\mathrm{Adj}_{(3,1)}$ and define a coherent adjunction in a strict $3$-category $\mathcal{C}$ as a map $\mathrm{Adj}_{(3,1)}\to\mathcal{C}$. We use string diagrams to show that any adjunction in $\mathcal{C}$ can be extended to a coherent adjunction in an essentially unique way. The results and their proofs will apply in the context of Gray $3$-categories after the string diagram calculus is shown to hold in that context in an upcoming paper.
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Cited by
[1] Viktoriya Ozornova and Martina Rovelli, "What is an equivalence in a higher category?", Bulletin of the London Mathematical Society 56 1, 1 (2024).
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