An Internal Language for Autonomous Categories

  • Ian Mackie
  • Leopoldo Román
  • Samson Abramsky
Conference paper
Part of the Workshops in Computing book series (WORKSHOPS COMP.)


In this extended abstract we present an internal language for symmetric monoidal closed (autonomous) categories analogous to the typed lambda calculus being an internal language for cartesian closed categories. The language we propose is the term assignment to the multiplicative fragment of Intuitionistic Linear Logic, which possesses exactly the right structure for an autonomous theory. We prove that this language is an internal language and show as an application the coherence theorem of Kelly and Mac Lane, which becomes straightforward to state and prove. We then hint at some further applications of this language; a further treatment will be given in the full paper.


Monoidal Category Linear Logic Internal Language Symmetric Monoidal Category Proof Term 
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Copyright information

© British Computer Society 1993

Authors and Affiliations

  • Ian Mackie
    • 1
  • Leopoldo Román
    • 1
  • Samson Abramsky
    • 1
  1. 1.Department of ComputingImperial CollegeLondonUK

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