Mathematics Research Blog

Research articles and notes in category theory, algebra, topology, and formalized mathematics.

Topological, Lax-Topological (Semi-Topological/Solid), and Topologically Algebraic Functors

December 25, 2025

Notes on topological, lax-topological (semi-topological/solid), and topologically algebraic functors via structured sources/sinks, classical characterizations, and the quantaloid-enriched “topological = total” theorem.

Reflections on the Right Use of Artificial Intelligence With a View to the Love of Mathematics

April 1, 2025

An essay on AI-generated mathematics through Meillassoux’s arche-fossil and Simone Weil’s account of attention.

Tarski's automorphisms

November 14, 2024

Notes on Tarski’s proposal that logical notions are those invariant under every automorphism of the universe of discourse.

Sheaves as Presheaves with an Equalizer Diagram

October 26, 2024

The sheaf axioms and their formulation as an equalizer diagram.

Monomorphisms and epimorphisms

December 17, 2022

Some basic properties and examples of monomorphisms, epimorphisms, and split morphisms.

hom-Sets

December 15, 2022

Some calculations with hom-sets and the covariant and contravariant hom-functors.

Describing difficult spaces

December 1, 2022

Topological spaces described through gluing diagrams, identification spaces, and geometric models.

Free semimodules and their examples

November 1, 2022

My honours project on free semimodules and their examples.

M-sets and Yoneda for monoids

July 15, 2022

M-sets, the Yoneda lemma for monoids, and the Yoneda embedding.

Free algebras by means of a universal property

June 27, 2022

Free algebras and their universal property, beginning with free vector spaces.