Higher Inductive Types as Homotopy-Initial Algebras
Abstract
Homotopy Type Theory is a new field of mathematics based on the surprising and elegant correspondence between Martin-Lofs constructive type theory and abstract homotopy theory. We have a powerful interplay between these disciplines - we can use geometric intuition to formulate new concepts in type theory and, conversely, use type-theoretic machinery to verify and often simplify existing mathematical proofs. A crucial ingredient in this new system are higher inductive types, which allow us to represent objects such as spheres, tori, pushouts, and quotients. We investigate a variant of higher inductive types whose computational behavior is determined up to a higher path. We show that in this setting, higher inductive types are characterized by the universal property of being a homotopy-initial algebra.
Keywords
Cite
@article{arxiv.1402.0761,
title = {Higher Inductive Types as Homotopy-Initial Algebras},
author = {Kristina Sojakova},
journal= {arXiv preprint arXiv:1402.0761},
year = {2014}
}