Pseudo-commutative monads and pseudo-closed 2-categories

Reference:

Hyland, M. and Power, J., 2002. Pseudo-commutative monads and pseudo-closed 2-categories. Journal of Pure and Applied Algebra, 175 (1-3), pp. 141-185.

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Official URL:

http://dx.doi.org/10.1016/S0022-4049(02)00133-0

Abstract

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

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