mathematics

ACT2020 conference notes: Main sessions

14 minute read

In the previous four posts I organized my notes from the ACT2020 Tutorial Day. In this post I’ll continue to note down things I’ve learned from the main sess...

Category theory notes 8: Functoriality

6 minute read

Fong & Spivak refer to category, functor, and natural transformation as the “big three” of category theory in their newly published textbook An Invitatio...

Category theory notes 7: Categorical idioms

8 minute read

Idioms and slangs are an important part of human language. They are short, expressive, and vividly reflect regional/historical mind-sets. And they are usuall...

Category theory notes 6: Think big

5 minute read

Category theory is spectacularly big. But exactly how big is it? Consider a set $A$. It can hold a huge number of elements, say, all grains of sand on Earth....

Category theory notes 5: Arrows and diagrams

7 minute read

Arrows are so vital to category theory that Awodey jokingly refers to the theory as “archery” (Category Theory, p. 2). Given two objects in a category, an ar...

Category theory notes 4: Monoid

8 minute read

Monoid is one of those concepts that are extremely simple, extremely useful, and can at the same time be extremely confusing. It was one of the first concept...