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Results tagged with homotopy-type-theory
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user 115253
The homotopy interpretation of constructive dependent type theory, the univalence axiom, higher inductive types, internal languages of higher toposes, univalent foundations for mathematics, and implementations of such theories in proof assistants.
5
votes
1
answer
183
views
Models for Higher Inductive Types in Homotopy Type Theory
Ordinary inductive types is initial algebras for free monads. However, HITs are not initial algebras for endofunctors but presented monads.
From nLab, initial algebra of a presentable (infinity,1)-m …
2
votes
1
answer
219
views
Synthetic type theory for virtual double category and its higher categories
For some monad T on a virtual equipment, the paper A unified framework for generalized multicategories by Cruttwell and Shulman (arXiv:0907.2460) proposes the normalized T-monoid.
Another paper, by …