What is...homotopy type theory?

Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.

This time.
What is...homotopy type theory? Or: HoTT = Ho + TT.

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Slides.
http://www.dtubbenhauer.com/youtube.html

TeX files for the presentation.
https://github.com/dtubbenhauer/My-Te...

Thumbnail.
https://c4.wallpaperflare.com/wallpap...
https://d2r55xnwy6nx47.cloudfront.net...

Main discussion.
https://arxiv.org/abs/2212.11082
https://web.archive.org/web/201707070...
https://www.ams.org/notices/201309/rn...
https://en.wikipedia.org/wiki/Homotop...
https://homotopytypetheory.org/book/
https://en.wikipedia.org/wiki/Homotop...
https://en.wikipedia.org/wiki/Higher_...
https://ncatlab.org/nlab/show/homotop...
https://homotopytypetheory.org/
https://golem.ph.utexas.edu/category/...

Background material.
https://en.wikipedia.org/wiki/Foundat...
https://en.wikipedia.org/wiki/Univale...
https://en.wikipedia.org/wiki/Intuiti...
https://en.wikipedia.org/wiki/Proof_a...
https://en.wikipedia.org/wiki/Automat...
https://en.wikipedia.org/wiki/Intuiti...
https://en.wikipedia.org/wiki/Mathema...
https://en.wikipedia.org/wiki/Structu...)
https://en.wikipedia.org/wiki/%E2%88%...
https://en.wikipedia.org/wiki/Simplic...
https://github.com/HoTT/Coq-HoTT

Computer talk.
https://github.com/thehottgame/TheHoT...
https://math.stackexchange.com/questi...

Pictures used.
Picture from    • What is...homotopy?  
https://uploads-ssl.webflow.com/5b1d4...
https://i.stack.imgur.com/3e0fj.png
Pictures from https://en.wikipedia.org/wiki/Homotop...
Picture from    • What is...homotopy of spheres?  
https://d2r55xnwy6nx47.cloudfront.net...

YouTube and co.
video.ias.edu/univalent/awodey
   • Homotopy Type Theory Discussed - Comp...  
   • Видео  

#categorytheory
#topology
#mathematics