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5. Identity & Inductive Types 49:00
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Constructing Quotient Inductive Inductive Types Information Guide

  1. Overview on Constructing Quotient Inductive Inductive Types
  2. Key Details
  3. Developments
  4. Detailed Analysis
  5. Summary

Overview on Constructing Quotient Inductive Inductive Types

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Key Details

Information Ambrus Kaposi, Quotient inductive-inductive types and higher friends Guide
Explore the main sources for Constructing Quotient Inductive Inductive Types.

Developments

TYPES2025 - 3.8. Thiago Felicissimo - Towards Quotient Inductive Types in Observational Type Theory Update
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Agda Lecture 8: Quotients and Higher Inductive Types in Cubical Agda -- HoTTEST Summer School 2022
Agda Lecture 8: Quotients and Higher Inductive Types in Cubical Agda -- HoTTEST Summer School 2022
Cubical Agda: A Dependently Typed Programming  Language with Univalence and Higher Inductive Types
Cubical Agda: A Dependently Typed Programming Language with Univalence and Higher Inductive Types
[POPL'22] Gradualizing the Calculus of Inductive Constructions
[POPL'22] Gradualizing the Calculus of Inductive Constructions
Inductive Construction
Inductive Construction
Quotient inductive types as categorified containers - Thorsten Altenkirch
Quotient inductive types as categorified containers - Thorsten Altenkirch
More on Higher Inductive Types
More on Higher Inductive Types
Niels van der Weide, Constructing 1-truncated finitary higher inductive types as groupoid quotients
Niels van der Weide, Constructing 1-truncated finitary higher inductive types as groupoid quotients
B5.E — Constructing Higher Inductive Types as Groupoid Quotients
B5.E — Constructing Higher Inductive Types as Groupoid Quotients
Higher Inductive Types in Cubical Computational Type Theory
Higher Inductive Types in Cubical Computational Type Theory
5. Identity & Inductive Types
5. Identity & Inductive Types
Type Theory in Type Theory Using Quotient Inductive Types
Type Theory in Type Theory Using Quotient Inductive Types

Detailed Analysis

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Last Updated: August 20, 2026

Summary

Full E5.C — Large and Infinitary Quotient Inductive-Inductive Types News
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