Homotopy Type Theory desired articles > history (Rev #35)

This page collects desired articles in the style of a TODO list. Feel free to edit and add your own wishes.

More on encode-decode

This method is used fruitfully in HoTT however can be a bit difficult to understand for beginners. Add some more articles detailing its use and generalisations. Specifically the proof of $\pi_1(S^1)$ and van kampen.

Group theory

Write out results of Higher Groups in Homotopy Type Theory. In particular outline how it can be linked with Localization in Homotopy Type Theory. Then we can finally start talking about localised cohomology.

Probability theory

Along the lines of Alex Simpson’s synthetic probability theory define the type of probability measures $\mathcal{M}_1(A)$ over a decidable type? $A$ and the set of random variable?s $RV(A)$ over $A$ in homotopy type theory.

Abstract Stone Duality

Attempt to translate the results in The Dedekind Reals in Abstract Stone Duality by Andrej Bauer and Paul Taylor into homotopy type theory. Might have to work with different universe levels.

 Higher observational type theory

• higher observational type theory