Jaques Carette Explores Unavoidable Mathematics in Universal Algebra & Category Theory 🔍

Taking for granted the constructions given to us by Universal Algebra and Category Theory, we can examine what mathematics (and computer science!) arises "for free". Even very simple theories give rise to a wealth of (known) derived material. Nevertheless, a systematic exploration has never been done. What is surprising is that rather simple theories give rise to scarcely known material. Furthermore mathematics of recent interest (eg: containers, lenses, inhabited spaces) arisenaturally. Subtle issues also crop up: Setoids, decidability both make an appearance.In other words, the simplicity is deceptive as a rich tapestry of concepts lies at the "low Kolmogorov complexity" end of theory exploration.