Pseudo-commutative monads and pseudo-closed 2-categories

AbstractPseudo-commutative 2-monads and pseudo-closed 2-categories are defined. The former give rise to the latter: if T is pseudo-commutative, then the 2-category T-Alg, of strict T-algebras and pseudo-maps of algebras, is pseudo-closed. In particular, the 2-category of symmetric monoidal categories, is pseudo-closed. Subject to a biadjointness condition that is satisfied by T-Alg, pseudo-closed structure induces pseudo-monoidal structure on the 2-category