Reflections on the Right Use of Artificial Intelligence With a View to the Love of Mathematics
How AI's capacity for mathematical discovery challenges traditional views of knowledge as being solely for us.
Mathematics Research Blog
Articles on category theory, universal algebra, topology, and the cultures around mathematics.
Tarski's automorphisms
Alfred Tarski considered 'logical notions' as those invariant under automorphisms of the universe of discourse.
Sheaves as Presheaves with an Equalizer Diagram
A note on sheaves.
Monomorphisms and epimorphisms
Exercises in category theory: monomorphisms and epimorphisms
hom-Sets
Exercises in category theory: hom-sets
Describing difficult spaces
A guide to describing and visualizing complex topological spaces such as tori, Klein bottles, and Möbius strips using gluing diagrams and geometric intuition. Explores identification spaces.
Free semimodules and their examples
Honours project on free semimodules and their examples. Covers definitions, universal properties, and connections to category theory and universal algebra. Supervised by Prof. G. Janelidze (UCT).
M-sets and Yoneda for monoids
Exercises in category theory: M-sets and the Yoneda lemma for monoids
Free algebras by means of a universal property
Exercises in category theory: free algebras by means of a universal property
Modules and Vector Spaces as Algebraic Categories
Exercises in category theory: category of modules and category of vector spaces as algebraic categories