Linearly distributive functors (1999) [10 citations — 7 self]
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Abstract:
Presented to Michael Barr to mark the occasion of his 60 th birthday This paper introduces a notion of \linear functor " between linearly distributive categories that is general enough to account for common structure in linear logic, such as the exponentials ( ! , ?), and the additives (product, coproduct), and yet when interpreted in the doctrine of -autonomous categories, gives the familiar notion of monoidal functor. We show that there is a bi-adjunction between the 2{categories of linearly distributive categories and linear functors, and of -autonomous categories and monoidal functors, given by the construction of the \nucleus " of a linearly distributive category. We develop a calculus of proof nets for linear functors, and show how linearity accounts for the essential coherence structure of the exponentials and the additives.
Citations
| 90 | What is a categorical model of intuitionistic linear logic – Bierman - 1995 |
| 76 | Weakly distributive categories – Cockett, Seely - 1997 |
| 52 | Natural deduction and coherence for weakly distributive categories,J. Pure and Applied Algebra 113 – Blute, Cockett, et al. - 1996 |
| 10 | Phase semantics for light linear logic – Kanovich, Okada, et al. |
| 1 | Non-symmetric -autonomous categories", Theoretical Computer Science 139 – Barr - 1995 |
| 1 | Weakly distributive categories", Journal of Pure and Applied Algebra 114 – Cockett, Seely - 1997 |
| 1 | Light linear logic", preprint – Girard - 1995 |
