# Category Theory Youtube Lectures by Bartosz Milewski ## Lecture 1 Watching [Category Theory 1.1: Motivation and Philosophy - YouTube](https://www.youtube.com/watch?v=I8LbkfSSR58&list=PLbgaMIhjbmEnaH_LTkxLI7FMa2HsnawM_), the very first introduction by [[Bartosz Milewski]]. He goes on about [[ZK - 3d1 - Mathematics is inherent to human beings, not the world]] ## Lecture 2 [Category Theory 1.2: What is a category? - YouTube](https://www.youtube.com/watch?v=p54Hd7AmVFU&list=PLbgaMIhjbmEnaH_LTkxLI7FMa2HsnawM_&index=2) When we abstract, we get rid of unnecessary details. Once details are gone, things that were different because of these details, they become identical. [[ZK - 3g2 - Abstraction removes details and makes things that were different, identical]] The three tools in the programmer's arsenal: - Abstraction - Composition - Identity "Identity, because of abstraction, is always nontrivial." There are different levels of equality: - strictly identical - identical for all intents and purposes [[Homotopy Type Theory]] tries to define if isomorphism is the same as identity. [[ZK - 3e0b - DEPREC - Composition and Identity define Category Theory]] We are describing the world in terms of spatial relationships invented by hunter gatherers [Category Theory 1.2: 11:07](https://youtu.be/p54Hd7AmVFU?t=667) and social language (objects and arrows). be aware of how the language constrains us.