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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... (Update)
Context of citations to this paper: More
...traditional logic, one adds a triple and cotriple, satisfying properties to be outlined below. This program was first outlined by Seely in [Se89]. Linear logic bears strong resemblance to linear algebra (from which it derives its name) but one significant difference is the...
...endofunctors which can be regarded as a composition of an adjoint pair [17] The observation that is just a comonad is due to R. Seely [27]. Indeed, if we limit ourselves to a special case, can be described in a very neat way. In short, given a closed monoidal category C,...
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5: Linear logic, coherence and dinaturality (context) - Blute - 1993
5: Weakly distributive categories - Cockett, Seely - 1991
4: Girard, J-Y. 1987. `Linear Logic'. In: Theoretical Computer Science 59, pp1-102.
BibTeX entry: (Update)
Seely, R.A.G. "Linear logic, -autonomous categories and cofree coalgebras", in J. Gray and A. Scedrov (eds.), Categories in Computer Science and Logic, Contemporary Mathematics 92 (Am. Math. Soc. 1989). http://citeseer.ist.psu.edu/seely89linear.html More
@inproceedings{ seely89linear,
author = "Robert A. G. Seely",
title = "Linear Logic, $*$-Autonomous Categories and Cofree Coalgebras",
booktitle = "Categories in Computer Science and Logic",
volume = "92",
publisher = "American Mathematical Society",
address = "Providence, Rhode Island",
editor = "John W. Gray and Andre Scedrov",
pages = "371--382",
year = "1989",
url = "citeseer.ist.psu.edu/seely89linear.html" }
Citations (may not include all citations):562 Categories for the working mathematician (context) - Lane - 1971
359 Introduction to higher order categorical logic (context) - Lambek, Scott - 1986
19 Multicategories revisited (context) - Lambek - 1987
13 Deductive systems and categories II (context) - Lambek - 1969
9 Springer Lecture Notes in Mathematics (context) - Barr, categories - 1979
6 Braided monoidal categories (context) - Joyal, Street - 1986
1 The Dialectica interpretation category (context) - de Paiva - 1987
The graph only includes citing articles where the year of publication is known.
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