Mathematics Research Blog
- 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.
- 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.
- Author Logic Test Post
Test post to verify author and tag display logic.
- 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