Noughts & Crosses: Cartesian Product [Intro to HoTT, No. 5, Part 1] 

Links and more: intro-hott.vid...
In this video, we take an informal look at what it means to "multiply" homotopy spaces. These "product types" play a central role in type theory, especially in the logic interpretation (as we'll discuss in a future video).
Video site for the series: intro-hott.video
RU-vid: • Intro to Homotopy Type...
Instagram: @Intro_HoTT
Formalization links:
- The formalization I'm developing for this video series: github.com/jac...
- More up-to-date HoTT formalization in Agda: github.com/Uni...
HoTT textbooks:
- The HoTT Book (2013) -- the original statement of HoTT: homotopytypeth...
- Introduction to Homotopy Type Theory, by Egbert Rijke (to be released): ncatlab.org/nl...
Image/audio credits:
- "Wholesome" by Kevin MacLeod (incompetech.com); CC BY 4.0 (creativecommon...)
- • Jazz Funk Piano Music ...
- Actam, CC BY-SA 4.0 (creativecommon..., via Wikimedia Commons
- en.wikipedia.o...)
- Augustus Binu, CC BY-SA 3.0 (creativecommon..., via Wikimedia Commons
- Djexplo, CC0, via Wikimedia Commons
- commons.wikime...
- Silsor, CC BY-SA 3.0 (creativecommons..., via Wikimedia Commons
Homotopy type theory (HoTT) is a new branch of type theory and a new foundation for mathematics. It serves as a common language for reasoning about computation (functional programming), about mathematical structure (synthetic homotopy theory and higher category theory), and about constructive logic. This Introduction to Homotopy Type Theory video lecture series is intended to explain what HoTT is, show how to work in HoTT (including how formalization in Agda works), and give intuition for why HoTT is the way it is. I don’t assume any particular background familiarity, but the more you know about mathematics, computer science, and logic, the more you’ll be able to get out of these videos. Enjoy!