Homotopy Type Theory: Univalent Foundations of Mathematics
Book
Foundational Source
Category Theory
Citation
The Univalent Foundations Program. (2013). Homotopy Type Theory: Univalent Foundations of Mathematics. Institute for Advanced Study.
Why this reference is included
Program’s Homotopy Type Theory: Univalent Foundations of Mathematics (2013), published by Institute for Advanced Study, sits in the program’s reference corpus as a standing technical source. Cited across Book I (Categorical Foundations), Part 18, Chapter The Self-Hosting Landscape; Book I (Categorical Foundations), Part 18, Chapter The Enrichment Frontier; Book I (Categorical Foundations), Part 18, Chapter Diagonal Resonance and Identity Slippage — the central framing is “Homotopy Type Theory provides the internal language of (∞,1)-toposes”.
Cited in
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Book I — Categorical Foundations Part 18Chapter The Self-Hosting Landscape
Homotopy Type Theory provides the internal language of (∞,1)-toposes
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Book I — Categorical Foundations Part 18Chapter The Enrichment Frontier
The HoTT Book demonstrates that the internal language of (∞,1)-toposes is homotopy type theory — a dependent type theory with univalence
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Book I — Categorical Foundations Part 18Chapter Diagonal Resonance and Identity Slippage
Component (L): Structural rules in the meta-theory. Homotopy Type Theory is formulated within a type theory that retains the standard structural rules