Category Theory Crash Course

First stop Yoneda's Lemma

What you'll learn
Objects, morphisms, functors and natural transformations
Universal properties
Yoneda's Lemma
The principle of abstraction and generality
Requirements
Familiarity with sets and functions would help
Familiarity with linear algebra and vector spaces would help more
In principle this could be taught first but slower
Description
Introduces the philosophy and basic results of category theory. The main one that has become quite well known is called Yoneda's Lemma and is a really fun way to apply the philosophy of category theory. We also have simple but fundamental notions in theory such as duality and universality which relate many of the constructions we knew about but perhaps didn't realise we related in this or that way. Will try to be a living course that grows with student participation.

Overview

Section 1: Introduction

Lecture 1 Introduction

Section 2: Ch1

Lecture 2 Objects and morphisms

Lecture 3 Universal properties

Lecture 4 Functors and Natural transformations

Lecture 5 Yoneda's Lemma

Lecture 6 Exercises

Advanced high school senior students who seek a proper foundation in maths,Undergraduate students who want to study graduate maths,Smart people who want to understand category theory for whatever purpose eg programming, research, etc,Fans of Grothendieck