Mathematics

Construct Colimits in a Topos Using Elementary Methods

Monday, Aug 4, 2025

An elementary topos is a category with finite limits, exponentials, and a subobject classifier $t:1\rightarrow\Omega$. We do not know from the definition that a topos has colimits. Surely we have …

Mathematical Structures in Programming Languages

Monday, Aug 4, 2025

If you enjoyed the Mathematical Structures in Logic course from last semester, you are going to love Nick’s rebranding for the new year: Mathematical Structures in Programming Languages! …

Mathematicians, list your ingredients!

Saturday, Aug 9, 2025

A wise friend of mine once compared being a constructivist to being a vegetarian: even if you are convinced it is the right choice, it is hard to fully commit to it in practice. As a vegetarian and a …

Regularity Properties of the Reals and the Axiom of Choice

Saturday, Aug 9, 2025

In this article, we aim to give an introduction to the set theoretic study (Jech 2003) of relation between regularity properties of the reals and the Axiom of Choice. Broadly conceived, regularity …

Rotating Shapes: The long(est) line

Monday, Aug 4, 2025

"The long line is a topological space somewhat similar to the real line, but in a certain sense ›longer‹." To understand this statement, we will firstly do a short recap of topology. A lot of …