Jets and differential linear logic
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Summary
It is proved that the category of vector bundles over a fixed smooth manifold and its corresponding category of convenient modules are models for intuitionistic differential linear logic and hence a computational theory of non-linear partial differential equations and their solutions based on variational calculus.
- Type
- article
- Published
- 2018-11-15
- Cited by
- 1
- References
- 62
- Access
- Open access
- OpenAlex
- https://openalex.org/W2900575161
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:53424343
Keywords
Morphism, Linear logic, Manifold (fluid mechanics), Differential (mechanical device), Interpretation (philosophy)
References
- D-Modules and Microlocal Calculus
- Bornologies and functional analysis : introductory course on the theory of duality topology-bornology and its use in functional analysis
- Categorical Models for Simply Typed Resource Calculi
- The Geometry of Jet Bundles
- Systems of partial differential equations and Lie pseudogroups
- Locally Presentable and Accessible Categories: Bibliography
- The Convenient Setting of Global Analysis
- JET SCHEMES, ARC SPACES AND THE NASH PROBLEM
- The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs
- A convenient differential category
- Descent in Locally Presentable Categories
- *-Autonomous categories and linear logic
- Uniformity and the Taylor expansion of ordinary lambda-terms
- Faisceaux algébriques cohérents
- On Köthe sequence spaces and linear logic
- Coherent Banach Spaces: a continuous denotational semantics
- On infinite-dimensional linear spaces
- Glueing and orthogonality for models of linear logic
- What is a categorical model of the differential and the resource λ-calculi?
- Full Intuitionistic Linear Logic (extended abstract)
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