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  • Mathematical Structures in Computer Science, Volume 19, Issue 2
  • April 2009, pp. 217-244

On traced monoidal closed categories

  • MASAHITO HASEGAWA (a1)
  • DOI: http://dx.doi.org/10.1017/S0960129508007184
  • Published online: 01 April 2009
Abstract

The structure theorem of Joyal, Street and Verity says that every traced monoidal category arises as a monoidal full subcategory of the tortile monoidal category Int. In this paper we focus on a simple observation that a traced monoidal category is closed if and only if the canonical inclusion from into Int has a right adjoint. Thus, every traced monoidal closed category arises as a monoidal co-reflexive full subcategory of a tortile monoidal category. From this, we derive a series of facts for traced models of linear logic, and some for models of fixed-point computation. To make the paper more self-contained, we also include various background results for traced monoidal categories.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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