Pseudo-commutative monads and pseudo-closed 2-categories (Q1850100)

\textit{A. Kock} [J. Austral. Math. Soc. 12, 405-424 (1971; Zbl 0244.18007)] considered commutative monads on symmetric closed monoidal categories and showed when their categories of algebras were also closed. The basic example is the monad on \({\mathcal S}et\) whose algebras are commutative monads. The present paper lifts this process to 2-categories where the basic example is the 2-monad on \({\mathcal C}at\) whose algebras are symmetric monoidal closed categories. The appropriate 2-category of algebras for a 2-monad has objects the strict algebras but only the pseudomorphisms.