I describe how mathematical functions can be visualized by:
(1) elements and arrows
(2) Wiring diagrams
(3) fibres
(4) bouquets
(5) graphs
(6) ontology logs
(7) categories
These ideas have applications throughout mathematics and beyond. Notable applications include set theory, cooking, planning, functional programming, dependent type theory, linguistics and category theory.
Category Theory For Beginners: Cooking, Monoidal Categories and Programming
https://www.youtube.com/watch?v=CYuG-wYx77o&list=PLCTMeyjMKRkoS699U0OJ3ymr3r01sI08l&index=25
Foundations 7: Dependent Type Theory
https://www.youtube.com/watch?v=Wh1QxF5FLJw
Category Theory For Beginners: Everyday Language
https://www.youtube.com/watch?v=MtJJGrCaLbI&list=PLCTMeyjMKRkoS699U0OJ3ymr3r01sI08l&index=9
Category Theory For Beginners: Introduction
https://www.youtube.com/watch?v=US4Zr1WKD-8&list=PLCTMeyjMKRkoS699U0OJ3ymr3r01sI08l&index=1