A Type Theory with a Tiny Object

Mitchell Riley

A Type Theory with a Tiny Object

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arxiv 2403.01939 v1 pith:PSKFQ6CP submitted 2024-03-04 math.CT cs.PLmath.LO

Mitchell Riley This is my paper · ORCID

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keywords typetheoryadjointobjecttinyapplicationscontainsdemonstrate

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We present an extension of Martin-L\"of 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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Projective Presentations of Lex Modalities
cs.LO 2025-01 conditional novelty 8.0 of 10

Presentations of topological modalities in HoTT yield internal sheaf conditions, local choice, and cohomology stability, applied to synthetic algebraic geometry and simplicial type theory.

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