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Category theory for linear logicians (2004)
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| Venue: | Linear Logic in Computer Science |
| Citations: | 13 - 2 self |
BibTeX
@INPROCEEDINGS{Blute04categorytheory,
author = {Richard Blute and Philip Scott},
title = {Category theory for linear logicians},
booktitle = {Linear Logic in Computer Science},
year = {2004},
pages = {3--64},
publisher = {University Press}
}
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Abstract
This paper presents an introduction to category theory with an emphasis on those aspects relevant to the analysis of the model theory of linear logic. With this in mind, we focus on the basic definitions of category theory and categorical logic. An analysis of cartesian and cartesian closed categories and their relation to intuitionistic logic is followed by a consideration of symmetric monoidal closed, linearly distributive and ∗-autonomous categories and their relation to multiplicative linear logic. We examine nonsymmetric monoidal categories, and consider them as models of noncommutative linear logic. We introduce traced monoidal categories, and discuss their relation to the geometry of interaction. The necessary aspects of the theory of monads is introduced in order to describe the categorical modelling of the exponentials. We conclude by briefly describing the notion of full completeness, a strong form of categorical completeness, which originated in the categorical model theory of linear logic. No knowledge of category theory is assumed, but we do assume knowledge of linear logic sequent calculus and the standard models of linear logic, and modest familiarity with typed lambda calculus. 0
Keyphrases
category theory linear logic linear logician categorical model theory strong form model theory categorical modelling cartesian closed category noncommutative linear logic traced monoidal category autonomous category symmetric monoidal categorical logic standard model necessary aspect intuitionistic logic categorical completeness nonsymmetric monoidal category modest familiarity basic definition linear logic sequent calculus typed lambda calculus full completeness
