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Linear Logic, *-Autonomous Categories and Cofree Coalgebras (1989)
| Venue: | IN CATEGORIES IN COMPUTER SCIENCE AND LOGIC |
| Citations: | 128 - 8 self |
BibTeX
@INPROCEEDINGS{Seely89linearlogic,,
author = {R.A.G. Seely},
title = {Linear Logic, *-Autonomous Categories and Cofree Coalgebras},
booktitle = {IN CATEGORIES IN COMPUTER SCIENCE AND LOGIC},
year = {1989},
pages = {371--382},
publisher = {American Mathematical Society}
}
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Abstract
A brief outline of the categorical characterisation of Girard's linear logic is given, analagous to the relationship between cartesian closed categories and typed -calculus. The linear structure amounts to a -autonomous category: a closed symmetric monoidal category G with finite products and a closed involution. Girard's exponential operator, ! , is a cotriple on G which carries the canonical comonoid structure on A with respect to cartesian product to a comonoid structure on !A with respect to tensor product. This makes the Kleisli category for ! cartesian closed.
Keyphrases
linear logic autonomous category cofree coalgebras finite product cartesian product qualitative domain primitive notion brief outline categorical characterisation jean-yves girard usual conditional canonical comonoid structure linear structure amount comonoid structure linear conditional gammaffi unary operator closed involution exponential operator closed symmetric monoidal category kleisli category logical system
