Induction principle of identity types of coequalizers

references.bib

@@ -251,6 +251,19 @@ @online{GGMS24
   keywords    = {Computer Science - Logic in Computer Science,Mathematics - Logic}
 }
 
+@inproceedings{KvR21,
+  title =        {Path spaces of higher inductive types in homotopy type theory},
+  author =       {Kraus, Nicolai and von Raumer, Jakob},
+  year =         {2021},
+  publisher =    {IEEE Press},
+  abstract =     {The study of equality types is central to homotopy type theory. Characterizing these types is often tricky, and various strategies, such as the encode-decode method, have been developed. We prove a theorem about equality types of coequalizers and pushouts, reminiscent of an induction principle and without any restrictions on the truncation levels. This result makes it possible to reason directly about certain equality types and to streamline existing proofs by eliminating the necessity of auxiliary constructions. To demonstrate this, we give a very short argument for the calculation of the fundamental group of the circle (Licata and Shulman [1]), and for the fact that pushouts preserve embeddings. Further, our development suggests a higher version of the Seifert-van Kampen theorem, and the set-truncation operator maps it to the standard Seifert-van Kampen theorem (due to Favonia and Shulman [2]). We provide a formalization of the main technical results in the proof assistant Lean.},
+  booktitle =    {Proceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science},
+  articleno =    {7},
+  numpages =     {13},
+  location =     {Vancouver, Canada},
+  series =       {LICS '19}
+}
+
 @article{KECA17,
   title       = {{Notions of Anonymous Existence in {{Martin-L\"of}} Type Theory}},
   author      = {Nicolai Kraus and Martín Escardó and Thierry Coquand and Thorsten Altenkirch},

src/synthetic-homotopy-theory.lagda.md

@@ -73,6 +73,7 @@ open import synthetic-homotopy-theory.functoriality-sequential-colimits public
 open import synthetic-homotopy-theory.functoriality-suspensions public
 open import synthetic-homotopy-theory.groups-of-loops-in-1-types public
 open import synthetic-homotopy-theory.hatchers-acyclic-type public
+open import synthetic-homotopy-theory.induction-principle-identity-types-coequalizers public
 open import synthetic-homotopy-theory.induction-principle-pushouts public
 open import synthetic-homotopy-theory.infinite-complex-projective-space public
 open import synthetic-homotopy-theory.infinite-cyclic-types public