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-TeX-files
Thumbnail.
https://c4.wallpaperflare.com/wallpaper/150/506/352/black-mathematics-logic-dark-background-wallpaper-preview.jpg
https://d2r55xnwy6nx47.cloudfront.net/uploads/2019/10/CategoryTheory-fig2c.jpg
Main discussion.
https://arxiv.org/abs/2212.11082
https://web.archive.org/web/20170707022332/https://hott.github.io/book/nightly/hott-a4-1075-g3c53219.pdf
https://www.ams.org/notices/201309/rnoti-p1164.pdf
https://en.wikipedia.org/wiki/Homotopy_type_theory
https://homotopytypetheory.org/book/
https://en.wikipedia.org/wiki/Homotopy_theory
https://en.wikipedia.org/wiki/Higher_category_theory
https://ncatlab.org/nlab/show/homotopy+type+theory
https://homotopytypetheory.org/
https://golem.ph.utexas.edu/category/2012/05/what_is_homotopy_type_theory_g.html
Background material.
https://en.wikipedia.org/wiki/Foundations_of_mathematics
https://en.wikipedia.org/wiki/Univalent_foundations
https://en.wikipedia.org/wiki/Intuitionistic_type_theory
https://en.wikipedia.org/wiki/Proof_assistant
https://en.wikipedia.org/wiki/Automated_theorem_proving
https://en.wikipedia.org/wiki/Intuitionistic_type_theory
https://en.wikipedia.org/wiki/Mathematical_logic
https://en.wikipedia.org/wiki/Structure_(mathematical_logic)
https://en.wikipedia.org/wiki/%E2%88%9E-groupoid
https://en.wikipedia.org/wiki/Simplicial_set
https://github.com/HoTT/Coq-HoTT
Computer talk.
https://github.com/thehottgame/TheHoTTGame
https://math.stackexchange.com/questions/419497/computer-algebra-system-for-category-theory
Pictures used.
Picture from https://www.youtube.com/watch?v=MOJ9XzMuFvk
https://uploads-ssl.webflow.com/5b1d427ae0c922e912eda447/5b552df044aced8aceb8f019_pic1.jpg
https://i.stack.imgur.com/3e0fj.png
Pictures from https://en.wikipedia.org/wiki/Homotopy_type_theory
Picture from https://www.youtube.com/watch?v=-3hGewm8qho
https://d2r55xnwy6nx47.cloudfront.net/uploads/2019/10/CategoryTheory-fig2c.jpg
YouTube and co.
video.ias.edu/univalent/awodey
https://www.youtube.com/watch?v=Ft8R3-kPDdk
https://www.youtube.com/watch?v=OupcXmLER7I
#categorytheory
#topology
#mathematics