Category theory notes 8: Functoriality
Fong & Spivak refer to category, functor, and natural transformation as the “big three” of category theory in their newly published textbook An Invitatio...
Recent posts
Category theory notes 7: Categorical idioms
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
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
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
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...