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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2 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 2representative citing papers
The thesis advances the development of synthetic homotopy theory within homotopy type theory, covering classifying types and internal questions not necessarily tied to classical homotopy.
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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.
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Classifying Types
The thesis advances the development of synthetic homotopy theory within homotopy type theory, covering classifying types and internal questions not necessarily tied to classical homotopy.