Homotopy Type Theory desired articles > history (Rev #25)

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.

Solèr’s theorem and the category of Hilbert spaces

Define the terms used to define and prove Solèr's theorem? in a constructive and predicative manner, and the terms used in the article HilbR to define the category of Hilbert spaces over the real numbers in a constructive and predicative manner.