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arXiv · 2510.15795

Synthetic perspectives on spaces and categories

Emily Riehl
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Abstract

Recently discovered domain-specific formal systems -- specifically homotopy type theory and simplicial type theory -- provide new perspectives on spaces and categories in a natively equivalence-invariant setting. In this note, we expose fundamental proof techniques from these parallel settings: describing induction principles over paths or arrows and constructions involving universes that are either univalent or directed univalent.

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Emily Riehl. 2025-10-17. Synthetic perspectives on spaces and categories. https://doi.org/10.1137/25m1806569

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