A Type Theory with a Tiny Object

March 04, 2024 · The Ethereal · 🏛 arXiv.org

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Authors Mitchell Riley arXiv ID 2403.01939 Category math.CT: Category Theory Cross-listed cs.PL, math.LO Citations 2 Venue arXiv.org Last Checked 1 month ago
Abstract
We present an extension of Martin-Löf Type Theory that contains a tiny object; a type for which there is a right adjoint to the formation of function types as well as the expected left adjoint. We demonstrate the practicality of this type theory by proving various properties related to tininess internally and suggest a few potential applications.
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