Category theory

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

25 Dec 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.

Sheaves as Presheaves with an Equalizer Diagram

26 Oct 2024

The sheaf axioms and their formulation as an equalizer diagram.

Monomorphisms and epimorphisms

17 Dec 2022

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

hom-Sets

15 Dec 2022

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

Free semimodules and their examples

01 Nov 2022

My honours project on free semimodules and their examples.

M-sets and Yoneda for monoids

15 Jul 2022

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

Free algebras by means of a universal property

27 Jun 2022

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

Modules and Vector Spaces as Algebraic Categories

26 Jun 2022

How modules and vector spaces can be described as algebraic categories.

Groupoids and skeletons of monoids and preorders

14 Jun 2022

Monoids and preorders as categories, and the corresponding groupoids and skeletons.

Exercises in category theory

14 Jun 2022

Series of posts containing short answers to exercises in category theory from my honours year at the University of Cape Town