Cocartesian fibrations are defined in synthetic simplicial type theory with closure properties proved using a novel equivalence between LARI adjunctions and initial sections.
Directed univalence in simplicial homotopy type theory
2 Pith papers cite this work. Polarity classification is still indexing.
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Presents directed first-order logic with asymmetric equality as relative left adjoint, polarity system for variances, and sound-complete semantics via directed doctrines; classical fragment complete in preorders.
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Fibrations in Directed Type Theory
Cocartesian fibrations are defined in synthetic simplicial type theory with closure properties proved using a novel equivalence between LARI adjunctions and initial sections.
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Doctrinal Semantics of Directed First-Order Logic
Presents directed first-order logic with asymmetric equality as relative left adjoint, polarity system for variances, and sound-complete semantics via directed doctrines; classical fragment complete in preorders.