Categorical models of Differential Linear Logic are expressed as pairs of Grothendieck fibrations equipped with a tangent functor by adapting type-theory semantics to linear-non-linear adjunctions, as a first step toward unifying DiLL with dependent types.
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Module-valued ODEs are defined via tensor products of Banach modules over finite-dimensional algebras, and the solution space of homogeneous linear cases is shown to be a finitely generated submodule.
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A Fibrational Perspective on Differential Linear Logic
Categorical models of Differential Linear Logic are expressed as pairs of Grothendieck fibrations equipped with a tangent functor by adapting type-theory semantics to linear-non-linear adjunctions, as a first step toward unifying DiLL with dependent types.
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Module-valued ordinary differential equations and structure of solution spaces
Module-valued ODEs are defined via tensor products of Banach modules over finite-dimensional algebras, and the solution space of homogeneous linear cases is shown to be a finitely generated submodule.