Category Archives: Uncategorized

Differential Geometry in Modal HoTT

As some of you might remember, back in 2015 at the meeting of the german mathematical society in Hamburg, Urs Schreiber presented three problems or “exercises” as he called it back then. There is a page about that on the … Continue reading

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A self-contained, brief and complete formulation of Voevodsky’s univalence axiom

I have often seen competent mathematicians and logicians, outside our circle, making technically erroneous comments about the univalence axiom, in conversations, in talks, and even in public material, in journals or the web. For some time I was a bit … Continue reading

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Impredicative Encodings of Inductive Types in HoTT

I recently completed my master’s thesis under the supervision of Steve Awodey and Jonas Frey. A copy can be found here. Known impredicative encodings of various inductive types in System F, such as the type of natural numbers do not … Continue reading

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In memoriam: Vladimir Voevodsky

https://www.ias.edu/news/2017/vladimir-voevodsky

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A hands-on introduction to cubicaltt

Some months ago I gave a series of hands-on lectures on cubicaltt at Inria Sophia Antipolis that can be found at: https://github.com/mortberg/cubicaltt/tree/master/lectures The lectures cover the main features of the system and don’t assume any prior knowledge of Homotopy Type … Continue reading

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Type theoretic replacement & the n-truncation

This post is to announce a new article that I recently uploaded to the arxiv: https://arxiv.org/abs/1701.07538 The main result of that article is a type theoretic replacement construction in a univalent universe that is closed under pushouts. Recall that in … Continue reading

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HoTT MRC

From June 4 — 10, 2017, there will be a workshop on homotopy type theory as one of the AMS’s Mathematical Research Communities (MRCs).

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